{"id":4344,"date":"2022-04-06T10:11:39","date_gmt":"2022-04-06T10:11:39","guid":{"rendered":"https:\/\/umschool.net\/library\/?p=4344"},"modified":"2023-02-28T15:58:43","modified_gmt":"2023-02-28T15:58:43","slug":"czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya","status":"publish","type":"post","link":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/","title":{"rendered":"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f"},"content":{"rendered":"\n<h3 class=\"has-text-align-center wp-block-heading\"><strong>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li>\u041a\u0430\u043a \u043d\u0435 \u043f\u0435\u0440\u0435\u043f\u0443\u0442\u0430\u0442\u044c \u0446\u0435\u043b\u043e\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0441 \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c?<\/li><li>\u0427\u0443\u0434\u043e-\u043c\u0435\u0442\u043e\u0434: \u043a\u0430\u043a \u043b\u0435\u0433\u043a\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u043b\u044e\u0431\u043e\u0435 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435?<\/li><li>\u0411\u0435\u0437 \u043a\u0430\u043a\u0438\u0445 \u0442\u0440\u0435\u0445 \u0431\u0443\u043a\u0432 \u043d\u0435 \u0441\u043f\u0440\u0430\u0432\u0438\u0442\u044c\u0441\u044f \u0441 \u0415\u0413\u042d?<\/li><\/ul>\n\n\n\n<p>\u0421\u0440\u0430\u0432\u043d\u0438\u0442\u044c \u0437\u0430\u0440\u043f\u043b\u0430\u0442\u0443 \u0438 \u0440\u0430\u0441\u0445\u043e\u0434\u044b, \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u043e\u0432 \u0432 \u0431\u043b\u044e\u0434\u0435 \u0438\u043b\u0438 \u0440\u0435\u0448\u0438\u0442\u044c, \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u043b\u0438\u0442\u043a\u0438 \u0432\u0437\u044f\u0442\u044c \u0434\u043b\u044f \u0440\u0435\u043c\u043e\u043d\u0442\u0430 \u0432 \u0432\u0430\u043d\u043d\u043e\u0439 \u2014 \u043c\u044b \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0433\u043e\u0440\u0430\u0437\u0434\u043e \u0447\u0430\u0449\u0435, \u0447\u0435\u043c \u043a\u0430\u0436\u0435\u0442\u0441\u044f. \u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u043f\u0440\u043e\u0434\u043e\u043b\u0436\u0438\u043c \u043d\u0430\u0448\u0435 \u0437\u043d\u0430\u043a\u043e\u043c\u0441\u0442\u0432\u043e \u0441 \u043c\u043d\u043e\u0433\u043e\u043e\u0431\u0440\u0430\u0437\u0438\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0438 \u043d\u0430\u0443\u0447\u0438\u043c\u0441\u044f \u0440\u0435\u0448\u0430\u0442\u044c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0438\u0437 \u0432\u0438\u0434\u043e\u0432.&nbsp;<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u0412\u0438\u0434\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439<\/strong><\/h2>\n\n\n\n<p>\u0412\u0441\u043f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f?&nbsp;<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\"><strong>\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> \u2014 \u044d\u0442\u043e \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e, \u0441\u043e\u0434\u0435\u0440\u0436\u0430\u0449\u0435\u0435 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0435, \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0435\u043d\u043d\u043e\u0435 \u0431\u0443\u043a\u0432\u043e\u0439.&nbsp;<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\"><strong>\u041a\u043e\u0440\u043d\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong> \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0442\u0430\u043a\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0433\u043e, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u0432\u0435\u0440\u043d\u044b\u043c \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e\u043c.&nbsp;<\/p>\n\n\n\n<p>\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0432 \u0432\u0438\u0434\u0435 \u0432\u0435\u0441\u043e\u0432: \u043d\u0430 \u043a\u0430\u0436\u0434\u043e\u0439 \u0447\u0430\u0448\u0435 \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c \u0447\u0442\u043e-\u0442\u043e \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u043e\u0435 \u043f\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044e. \u0415\u0441\u043b\u0438 \u0436\u0435 \u0432\u0435\u0441\u044b \u043d\u0435 \u043d\u0430\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u0432 \u0440\u0430\u0432\u043d\u043e\u0432\u0435\u0441\u0438\u0438, \u0442\u043e \u043f\u0435\u0440\u0435\u0434 \u043d\u0430\u043c\u0438 \u0431\u0443\u0434\u0435\u0442 \u0443\u0436\u0435 \u043d\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435.&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/15-13-1024x918.png\" alt=\"\" class=\"wp-image-23320\" width=\"256\" height=\"230\" srcset=\"\/library\/wp-content\/uploads\/2023\/02\/15-13-1024x918.png 1024w, \/library\/wp-content\/uploads\/2023\/02\/15-13-300x269.png 300w, \/library\/wp-content\/uploads\/2023\/02\/15-13-768x688.png 768w, \/library\/wp-content\/uploads\/2023\/02\/15-13-1536x1376.png 1536w, \/library\/wp-content\/uploads\/2023\/02\/15-13-2048x1835.png 2048w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p>\u0412 \u0441\u0442\u0430\u0442\u044c\u0435 \u00ab<a href=\"https:\/\/umschool.net\/library\/matematika\/linejnye-kvadratnye-i-kubicheskie-uravneniya-2\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u041b\u0438\u043d\u0435\u0439\u043d\u044b\u0435, \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0435 \u0438 \u043a\u0443\u0431\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/a>\u00bb \u043c\u044b \u0443\u0436\u0435 \u043d\u0430\u0447\u0430\u043b\u0438 \u0440\u0430\u0437\u0431\u0438\u0440\u0430\u0442\u044c\u0441\u044f \u0432 \u043d\u0438\u0445. \u041d\u0430\u0441\u0442\u0430\u043b\u043e \u0432\u0440\u0435\u043c\u044f \u043d\u0435\u043c\u043d\u043e\u0433\u043e \u0443\u0441\u043b\u043e\u0436\u043d\u0438\u0442\u044c \u0437\u0430\u0434\u0430\u0447\u0443.&nbsp;<\/p>\n\n\n\n<p>\u041a\u0430\u043a\u0438\u0435 \u0435\u0449\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0431\u044b\u0432\u0430\u044e\u0442?&nbsp;<\/p>\n\n\n\n<p>\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c <strong>\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c\u0438<\/strong> \u0438 <strong>\u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c\u0438<\/strong>. \u0412\u0441\u043f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u044c \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0441\u0442\u044c \u043c\u044b \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u043b\u0438 \u0432 \u0447\u0438\u0441\u043b\u0430\u0445.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>\u0420\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430 \u2014 <\/strong>\u044d\u0442\u043e \u0447\u0438\u0441\u043b\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0432 \u0432\u0438\u0434\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0439 \u0434\u0440\u043e\u0431\u0438. <em>\u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440,<\/em>&nbsp; 12.<\/li><li><strong>\u0418\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430 \u2014 <\/strong>\u044d\u0442\u043e \u0447\u0438\u0441\u043b\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043d\u0435 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c\u0438. \u042d\u0442\u043e \u0431\u0435\u0441\u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0435 \u043d\u0435\u043f\u0435\u0440\u0438\u043e\u0434\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0434\u0435\u0441\u044f\u0442\u0438\u0447\u043d\u044b\u0435 \u0434\u0440\u043e\u0431\u0438. <em>\u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, <\/em>2,2360679775. \u0418\u043c\u0435\u043d\u043d\u043e \u0432 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u043b\u0430\u0445 \u043c\u044b \u0441\u0442\u0430\u043b\u043a\u0438\u0432\u0430\u0435\u043c\u0441\u044f \u0441 \u043a\u043e\u0440\u043d\u044f\u043c\u0438 \u0438\u043b\u0438 \u043d\u0435\u0446\u0435\u043b\u044b\u043c\u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u044f\u043c\u0438.&nbsp;<\/li><\/ul>\n\n\n\n<p><em>\u041c\u0438\u043d\u0443\u0442\u043a\u0430 \u0440\u0443\u0441\u0441\u043a\u043e\u0433\u043e \u044f\u0437\u044b\u043a\u0430! <\/em><strong><em>\u041a\u0430\u043a \u043f\u0440\u043e\u0449\u0435 \u0437\u0430\u043f\u043e\u043c\u043d\u0438\u0442\u044c \u043e\u0442\u043b\u0438\u0447\u0438\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b? <\/em><\/strong><em>\u0412\u0441\u043f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e \u0441\u043b\u043e\u0432\u043e \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0439 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u043e \u043e\u0442 \u00ab\u0440\u0430\u0446\u0438\u043e\u00bb \u2014 \u0440\u0430\u0437\u0443\u043c\u043d\u044b\u0439. \u0418\u043d\u044b\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430 \u2014 \u044d\u0442\u043e \u00ab\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u0435\u00bb \u0438 \u00ab\u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u044b\u0435\u00bb \u0447\u0438\u0441\u043b\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0442\u043e\u0447\u043d\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c. \u0418\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430 \u0436\u0435, \u0432 \u0441\u0432\u043e\u044e \u043e\u0447\u0435\u0440\u0435\u0434\u044c, \u00ab\u043d\u0435\u043b\u043e\u0433\u0438\u0447\u043d\u044b\u0435\u00bb, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0438\u0445 \u043d\u0430\u043c\u043d\u043e\u0433\u043e \u0442\u044f\u0436\u0435\u043b\u0435\u0435 (\u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0447\u0435\u043c\u0443 \u0442\u043e\u0447\u043d\u043e \u0440\u0430\u0432\u0435\u043d <\/em>\\(\\sqrt3\\)<em>?).&nbsp;<\/em><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/12-18-1024x968.png\" alt=\"\" class=\"wp-image-23321\" width=\"512\" height=\"484\" srcset=\"\/library\/wp-content\/uploads\/2023\/02\/12-18-1024x968.png 1024w, \/library\/wp-content\/uploads\/2023\/02\/12-18-300x284.png 300w, \/library\/wp-content\/uploads\/2023\/02\/12-18-768x726.png 768w, \/library\/wp-content\/uploads\/2023\/02\/12-18-1536x1453.png 1536w, \/library\/wp-content\/uploads\/2023\/02\/12-18-2048x1937.png 2048w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p><strong>\u0420\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f <\/strong>\u0434\u0435\u043b\u044f\u0442\u0441\u044f \u043d\u0430:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\u0446\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438<\/li><li>\u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435.<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/1_logo-1-1024x463.png\" alt=\"\" class=\"wp-image-23322\" width=\"512\" height=\"232\" srcset=\"\/library\/wp-content\/uploads\/2023\/02\/1_logo-1-1024x463.png 1024w, \/library\/wp-content\/uploads\/2023\/02\/1_logo-1-300x136.png 300w, \/library\/wp-content\/uploads\/2023\/02\/1_logo-1-768x347.png 768w, \/library\/wp-content\/uploads\/2023\/02\/1_logo-1.png 1202w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p>\u0418\u0442\u0430\u043a, \u0442\u0435\u043f\u0435\u0440\u044c, \u043a\u043e\u0433\u0434\u0430 \u043c\u044b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u043b\u0438\u0441\u044c \u0441 \u0432\u0438\u0434\u0430\u043c\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u043d\u0430\u0441\u0442\u0430\u043b\u043e \u0432\u0440\u0435\u043c\u044f \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u043a\u0430\u0436\u0434\u044b\u0439 \u0438\u0437 \u043d\u0438\u0445 \u0447\u0443\u0442\u044c \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u0435\u0435.&nbsp;<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong><\/h2>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\"><strong>\u0426\u0435\u043b\u043e\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> \u2014 \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0435\u0441\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0435, \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435, \u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438 \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0446\u0435\u043b\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c.<\/p>\n\n\n\n<p>\u0422\u0430\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043c\u043e\u0436\u0435\u0442 \u044f\u0432\u043b\u044f\u0442\u044c\u0441\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u043c, \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u043c \u0438\u043b\u0438 \u0434\u0440\u0443\u0433\u0438\u043c \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c. \u0414\u043b\u044f \u0442\u0435\u0445, \u043a\u0442\u043e \u0435\u0449\u0435 \u043d\u0435 \u0443\u0441\u043f\u0435\u043b \u0441 \u043d\u0438\u043c\u0438 \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u0442\u044c\u0441\u044f, \u043c\u044b \u043d\u0430\u043f\u0438\u0441\u0430\u043b\u0438 \u0441\u0442\u0430\u0442\u044c\u044e \u00ab<a href=\"https:\/\/umschool.net\/library\/matematika\/linejnye-kvadratnye-i-kubicheskie-uravneniya-2\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u041b\u0438\u043d\u0435\u0439\u043d\u044b\u0435, \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0435 \u0438 \u043a\u0443\u0431\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/a>\u00bb.<\/p>\n\n\n\n<p>\u0412\u0438\u0434 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">f(x) = 0, \u0433\u0434\u0435<br><br>f(x) \u2014 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u0417\u0430\u043c\u0435\u0442\u0438\u043c, \u0447\u0442\u043e \u0432\u043c\u0435\u0441\u0442\u043e <em>f(x)<\/em> \u043c\u043e\u0436\u0435\u0442 \u0441\u0442\u043e\u044f\u0442\u044c \u043b\u044e\u0431\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0441 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0446\u0435\u043b\u044b\u043c\u0438 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\u043c\u0438 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f:<\/p>\n\n\n\n<p>\\(32x-15=0\\);<br>\\(3x-2=2x+3\\);<br>\\(57x(x+8)(33x-11)=10x\\).<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/13-16-835x1024.png\" alt=\"\" class=\"wp-image-23323\" width=\"418\" height=\"512\" srcset=\"\/library\/wp-content\/uploads\/2023\/02\/13-16-835x1024.png 835w, \/library\/wp-content\/uploads\/2023\/02\/13-16-245x300.png 245w, \/library\/wp-content\/uploads\/2023\/02\/13-16-768x942.png 768w, \/library\/wp-content\/uploads\/2023\/02\/13-16-1253x1536.png 1253w, \/library\/wp-content\/uploads\/2023\/02\/13-16-1670x2048.png 1670w\" sizes=\"auto, (max-width: 418px) 100vw, 418px\" \/><\/figure><\/div>\n\n\n\n<p><strong>\u041a\u0430\u043a \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0440\u0435\u0448\u0430\u0442\u044c \u0442\u0430\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f?<\/strong><\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\"><strong>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong><br><br>1. \u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0442\u0438 \u0432\u0441\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u0438\u0437 \u043f\u0440\u0430\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0438 \u0432 \u043b\u0435\u0432\u0443\u044e, \u0447\u0442\u043e\u0431\u044b \u0441\u043f\u0440\u0430\u0432\u0430 \u0431\u044b\u043b \u0442\u043e\u043b\u044c\u043a\u043e \u043d\u043e\u043b\u044c.<br>2. \u0421\u043e\u0432\u0435\u0440\u0448\u0438\u0442\u044c \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u0434\u043b\u044f \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043a \u043e\u0431\u044b\u0447\u043d\u043e\u043c\u0443 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u043e\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e (\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0435, \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435, \u043a\u0443\u0431\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0438 \u0442.\u0434.).<br>3. \u0420\u0435\u0448\u0438\u0442\u044c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0438 \u043d\u0430\u0439\u0442\u0438 \u043a\u043e\u0440\u043d\u0438.<\/p>\n\n\n\n<p>\u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u0438\u0441\u0442\u0443\u043f\u0438\u043c \u043a \u0441\u0430\u043c\u043e\u043c\u0443 \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u043e\u043c\u0443: \u0440\u0435\u0448\u0435\u043d\u0438\u044e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439. \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(\\frac{x^2-1}{8}=10\\)<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c 10 \u0432 \u043b\u0435\u0432\u0443\u044e \u0447\u0430\u0441\u0442\u044c. \u041e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043f\u043e\u043c\u0435\u043d\u044f\u0435\u043c \u0437\u043d\u0430\u043a \u043d\u0430 \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u044b\u0439: \u0435\u0441\u043b\u0438 \u043c\u044b \u043e\u0442\u043d\u0438\u043c\u0430\u0435\u043c \u0447\u0442\u043e-\u0442\u043e \u043e\u0442 \u043e\u0434\u043d\u043e\u0439 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u0442\u043e \u043e\u0431\u044f\u0437\u0430\u043d\u044b \u043e\u0442\u043d\u044f\u0442\u044c \u0442\u0430\u043a\u043e\u0435 \u0436\u0435 \u0447\u0438\u0441\u043b\u043e \u0438 \u043e\u0442 \u0434\u0440\u0443\u0433\u043e\u0439.&nbsp;<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\">\\(\\frac{x^2-1}{8}-10=0\\)<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\"><li>\u0414\u043e\u043c\u043d\u043e\u0436\u0438\u043c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 8, \u0447\u0442\u043e\u0431\u044b \u0438\u0437\u0431\u0430\u0432\u0438\u0442\u044c\u0441\u044f \u043e\u0442 \u0434\u0440\u043e\u0431\u0438.<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\">\\(8*(\\frac{x^2-1}{8}-10)=0*8\\)<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\"><li>\u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0441\u043a\u043e\u0431\u043a\u0438 \u0438 \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043c <a href=\"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/#\u0442\u0435\u0440\u043c\u0438\u043d\u044b\" target=\"_blank\" rel=\"noreferrer noopener\">\u043f\u043e\u0434\u043e\u0431\u043d\u044b\u0435<\/a> \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435, \u0442\u043e \u0435\u0441\u0442\u044c \u0441\u043b\u043e\u0436\u0438\u043c \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u0441 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u043e\u0439 \u0431\u0443\u043a\u0432\u0435\u043d\u043d\u043e\u0439 \u0447\u0430\u0441\u0442\u044c\u044e.<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\">\\(x^2-1-80=0\\)<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(x^2-81=0\\)<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\"><li>\u0420\u0435\u0448\u0438\u043c \u043d\u0435\u043f\u043e\u043b\u043d\u043e\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435.&nbsp;<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\">\\(x^2=81\\)<\/p>\n\n\n\n<p>\u0418\u0437\u0432\u043b\u0435\u0447\u0435\u043c \u043a\u043e\u0440\u0435\u043d\u044c \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043c x=\u00b19. \u041c\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u0438 \u0434\u0432\u0430 \u0447\u0438\u0441\u043b\u0430, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043f\u0440\u0438 \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0438 \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0438 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435, \u0438 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430 \u0441\u0442\u0430\u043d\u043e\u0432\u044f\u0442\u0441\u044f \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c\u0438: \\(9^2=9*9=81\\) \u0438 \\((-9)^2=(-9)*(-9)=81\\).<\/p>\n\n\n\n<p>\u041a\u0430\u043a \u043c\u044b \u0443\u0436\u0435 \u0441\u043a\u0430\u0437\u0430\u043b\u0438, \u0435\u0441\u0442\u044c \u0446\u0435\u043b\u044b\u0435 \u0438 \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. \u0422\u0430\u043a \u0432 \u0447\u0435\u043c \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u044c \u0432\u0442\u043e\u0440\u044b\u0445?&nbsp;<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u0414\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong><\/h2>\n\n\n\n<p><strong>\u0414\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> \u2014 \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0443 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0445\u043e\u0442\u044f \u0431\u044b \u0432 \u043e\u0434\u043d\u043e\u0439 \u0434\u0440\u043e\u0431\u0438 \u0432 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435 \u0435\u0441\u0442\u044c \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0430\u044f.<\/p>\n\n\n\n<p>\u0412\u0438\u0434 \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">\\(\\frac{f(x)}{g(x)}=0\\), \u0433\u0434\u0435<br><br>\\(f(x)\\) \u0438 \\(g(x)\\) \u2014 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0441 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0439 <em>\u0445.<\/em><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u041a\u0430\u043a \u043f\u043e\u043d\u044f\u0442\u043d\u043e \u0438\u0437 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f, \u0432 \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u043d\u0435 \u043f\u0440\u043e\u0441\u0442\u043e \u0438\u043c\u0435\u0442\u044c \u0434\u0440\u043e\u0431\u044c, \u0432 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0434\u043e\u043b\u0436\u043d\u0430 \u0431\u044b\u0442\u044c \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f. \u0418\u043d\u044b\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043c\u044b \u0434\u0435\u043b\u0438\u043c \u0447\u0442\u043e-\u043b\u0438\u0431\u043e \u043d\u0430 \u0431\u0443\u043a\u0432\u0435\u043d\u043d\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u041a\u0430\u043a \u043d\u0435 \u043f\u0435\u0440\u0435\u043f\u0443\u0442\u0430\u0442\u044c \u0446\u0435\u043b\u043e\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0441 \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c?<\/strong><br><br>\u0415\u0441\u043b\u0438 <em>\u0445<\/em> \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u0442\u043e\u043b\u044c\u043a\u043e <strong>\u0432 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u0435 \u0434\u0440\u043e\u0431\u0438<\/strong>, \u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u2014 \u0446\u0435\u043b\u043e\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435.<br><br>\u0415\u0441\u043b\u0438 <em>\u0445<\/em> \u0435\u0441\u0442\u044c <strong>\u0432 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435<\/strong> <strong>\u0434\u0440\u043e\u0431\u0438<\/strong>, \u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u2014 \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435.<br><br>\u0412 \u044d\u0442\u043e\u043c \u0438\u0445 \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0435 \u043e\u0442\u043b\u0438\u0447\u0438\u0435.<br>&nbsp;<br><strong>\u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440:<\/strong> \\(\\frac{12}{7-x}=x\\) \u2014 \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0430 \u0432\u043e\u0442 \\(\\frac{12-x}{7}=x\\) \u2014 \u0446\u0435\u043b\u043e\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435.<br><br>\u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \\(\\frac{x}{2}=\\frac{1+x}{5}\\) \u2014 \u0446\u0435\u043b\u043e\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0430 \\(\\frac{x^{-1}}{2}=\\frac{1+x}{5}\\) \u2014 \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435. \u0417\u0430\u043c\u0435\u0442\u0438\u043c, \u0447\u0442\u043e \u0432\u0442\u043e\u0440\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u0435\u0440\u0435\u043f\u0438\u0441\u0430\u0442\u044c \u0432 \u0432\u0438\u0434\u0435 \\(\\frac{1}{2x}=\\frac{1+x}{5}\\).<br><br>\u041c\u043e\u0436\u0435\u0442 \u0432\u043e\u0437\u043d\u0438\u043a\u043d\u0443\u0442\u044c \u0432\u043e\u043f\u0440\u043e\u0441: \u0430 \u043a\u0430\u043a \u043c\u044b \u043f\u0435\u0440\u0435\u0432\u0435\u0440\u043d\u0443\u043b\u0438 \u0434\u0440\u043e\u0431\u044c? \u0412 \u0441\u043b\u0443\u0447\u0430\u0435 \u0435\u0441\u043b\u0438 \u0434\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u043d\u0435\u043f\u043e\u043d\u044f\u0442\u043d\u043e \u0434\u043b\u044f \u0432\u0430\u0441, \u0441\u0442\u043e\u0438\u0442 \u043e\u0437\u043d\u0430\u043a\u043e\u043c\u0438\u0442\u044c\u0441\u044f \u0441\u043e \u0441\u0442\u0430\u0442\u044c\u0435\u0439 \u00ab<a href=\"https:\/\/umschool.net\/library\/matematika\/dejstviya-s-naturalnymi-chislami\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0414\u0435\u0439\u0441\u0442\u0432\u0438\u044f \u0441 \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u044b\u043c\u0438 \u0447\u0438\u0441\u043b\u0430\u043c\u0438<\/a>\u00bb.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u0421\u043e\u0441\u0442\u0430\u0432\u0438\u043c \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u044f. \u0412 \u044d\u0442\u043e\u0442 \u0440\u0430\u0437 \u043d\u0430\u043c \u043f\u043e\u0442\u0440\u0435\u0431\u0443\u0435\u0442\u0441\u044f \u0447\u0443\u0442\u044c \u0431\u043e\u043b\u044c\u0448\u0435 \u0448\u0430\u0433\u043e\u0432, \u0447\u0435\u043c \u0432 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435.&nbsp;<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\"><strong>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong><br><br>1. \u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0442\u0438 \u0432\u0441\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u0438\u0437 \u043f\u0440\u0430\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0438 \u0432 \u043b\u0435\u0432\u0443\u044e, \u0435\u0441\u043b\u0438 \u043e\u043d\u0438 \u0435\u0441\u0442\u044c, \u0447\u0442\u043e\u0431\u044b \u0441\u043f\u0440\u0430\u0432\u0430 \u0431\u044b\u043b \u0442\u043e\u043b\u044c\u043a\u043e \u043d\u043e\u043b\u044c.<br>2. \u0421\u043b\u0435\u0432\u0430 \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f, \u0435\u0441\u043b\u0438 \u043d\u0443\u0436\u043d\u043e.<br>3. \u041f\u0440\u0438\u0432\u0435\u0441\u0442\u0438 \u0432\u0441\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u0441\u043b\u0435\u0432\u0430 \u043a \u043e\u0431\u0449\u0435\u043c\u0443 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044e \u0438 \u0437\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u0432 \u0432\u0438\u0434\u0435 \u0434\u0440\u043e\u0431\u0438.<br>4. \u0417\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u0441\u0438\u0441\u0442\u0435\u043c\u0443, \u0433\u0434\u0435 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c \u044d\u0442\u043e\u0439 \u0434\u0440\u043e\u0431\u0438 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e, \u0430 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043d\u0435 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e.<br>5. \u0420\u0435\u0448\u0438\u0442\u044c \u0441\u0438\u0441\u0442\u0435\u043c\u0443.<\/p>\n\n\n\n<p>\u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u0434\u0430\u043d\u043d\u043e\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u0435:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(\\frac{x^2+2x-9}{x-2}-1=\\frac{x+4}{2}\\).<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \u0432\u0441\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u0432 \u043b\u0435\u0432\u0443\u044e \u0447\u0430\u0441\u0442\u044c. \u041d\u0435 \u0437\u0430\u0431\u044b\u0432\u0430\u0435\u043c \u043c\u0435\u043d\u044f\u0442\u044c \u0437\u043d\u0430\u043a\u0438 \u043f\u0440\u0438 \u043f\u0435\u0440\u0435\u043d\u043e\u0441\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0445 \u0447\u0435\u0440\u0435\u0437 \u0437\u043d\u0430\u043a \u0440\u0430\u0432\u043d\u043e.&nbsp;<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\">\\(\\frac{x^2+2x-9}{x-2}-1-\\frac{x+4}{2}=0\\)<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\"><li>\u041f\u0440\u0438\u0432\u0435\u0434\u0435\u043c \u043a \u043e\u0431\u0449\u0435\u043c\u0443 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044e. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043a\u0430\u0436\u0434\u0443\u044e \u0434\u0440\u043e\u0431\u044c \u0434\u043e\u043c\u043d\u043e\u0436\u0438\u043c \u043d\u0430 \u0442\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0435\u0439 \u00ab\u043d\u0435 \u0445\u0432\u0430\u0442\u0430\u0435\u0442\u00bb \u0432 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435.<\/li><\/ol>\n\n\n\n<p>\u0412 \u043d\u0430\u0448\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043e\u0431\u0449\u0438\u0439 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u0431\u0443\u0434\u0435\u0442 \\(2(x-2)\\):<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(\\frac{x^2+2x-9}{x-2}*2-1*2(x-2)-\\frac{x+4}{2}*(x-2)=0\\)<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(\\frac{2(x^2+2x-9)-2(x-2)-(x+4)(x-2)}{2(x-2)}=0\\)<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\"><li>\u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0441\u043a\u043e\u0431\u043a\u0438 \u0432 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u0435:<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\">\\(\\frac{2x^2+4x-18-2x+4-x^2+2x-4x+8}{2(x-2)}=0\\).<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\"><li>\u0421\u043b\u043e\u0436\u0438\u043c <a href=\"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/#\u0442\u0435\u0440\u043c\u0438\u043d\u044b\" target=\"_blank\" rel=\"noreferrer noopener\">\u043f\u043e\u0434\u043e\u0431\u043d\u044b\u0435<\/a> \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435:<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\">\\(\\frac{(2x^2-x^2)+(4x-2x+2x-4x)+(-18+4+8)}{2(x-2)}=0\\)<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(\\frac{x^2-6}{2(x-2)}=0\\)<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\"><li>\u0412\u0441\u043f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c \u0434\u043e\u043b\u0436\u0435\u043d \u0431\u044b\u0442\u044c \u0440\u0430\u0432\u0435\u043d 0, \u0430 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043d\u0435 \u0440\u0430\u0432\u0435\u043d. <strong>\u0417\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u043d\u0438\u043a\u043e\u0433\u0434\u0430 \u043d\u0435 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u0435\u043d 0, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043d\u0430 0 \u0434\u0435\u043b\u0438\u0442\u044c \u043d\u0435\u043b\u044c\u0437\u044f. <\/strong>\u0417\u0430\u043f\u0438\u0448\u0435\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439:<\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/2_logo.png\" alt=\"\" class=\"wp-image-23331\" width=\"154\" height=\"63\" srcset=\"\/library\/wp-content\/uploads\/2023\/02\/2_logo.png 307w, \/library\/wp-content\/uploads\/2023\/02\/2_logo-300x123.png 300w\" sizes=\"auto, (max-width: 154px) 100vw, 154px\" \/><\/figure><\/div>\n\n\n\n<p>\u0420\u0435\u0448\u0438\u043c \u043a\u0430\u0436\u0434\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435.&nbsp;<\/p>\n\n\n\n<p>\\(x^2-6=0 =&gt; x^2=6 =&gt; x=\\pm\\sqrt6\\)<\/p>\n\n\n\n<p>\\(2(x-2)\\neq0\\), \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043a\u0430\u0436\u0434\u044b\u0439 \u043c\u043d\u043e\u0436\u0438\u0442\u0435\u043b\u044c \u043d\u0435 \u0440\u0430\u0432\u0435\u043d 0. \u0422\u043e\u0433\u0434\u0430 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c, \u0447\u0442\u043e \\(x-2\\neq0 =&gt; x\\neq2\\).&nbsp;<\/p>\n\n\n\n<p>\u0420\u0435\u0448\u0435\u043d\u0438\u0435\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0435 \u0431\u0443\u0434\u0435\u0442 \\(x=\\pm\\sqrt6\\), \u044d\u0442\u043e \u0438 \u0435\u0441\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u0418\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong><\/h2>\n\n\n\n<p>\u041c\u044b \u0443\u0436\u0435 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438 \u0434\u0432\u0430 \u0432\u0438\u0434\u0430 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u043f\u0435\u0440\u0435\u0439\u0434\u0435\u043c \u043a \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c.<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\"><strong>\u0418\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> \u2014 \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0443\u044e \u043f\u043e\u0434 \u043a\u043e\u0440\u043d\u0435\u043c \u0438\u043b\u0438 \u043e\u043d\u0430 \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u0430 \u0432 \u0434\u0440\u043e\u0431\u043d\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c.<\/p>\n\n\n\n<p>\u0418\u043c\u0435\u043d\u043d\u043e \u043d\u0430\u043b\u0438\u0447\u0438\u0435\u043c \u043a\u043e\u0440\u043d\u044f \u0438\u043b\u0438 \u0434\u0440\u043e\u0431\u043d\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u043e\u0445\u043e\u0436\u0438 \u043d\u0430 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0447\u0438\u0441\u043b\u0430.&nbsp;<\/p>\n\n\n\n<p>\u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440: \\(\\sqrt{10 -x}=x-4; x^{\\frac{2}{3}}=4\\) \u2014 \u044d\u0442\u043e \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f.<\/p>\n\n\n\n<p>\u0418\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u0438\u0445 \u0432\u0438\u0434\u043e\u0432:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">1) \\(\\sqrt{f(x)}=g(x)\\)<br>2) \\(\\sqrt{f(x)}=\\sqrt{g(x)}\\)<br>\u0420\u0430\u0437\u043d\u044b\u0435 \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u043a\u043e\u0440\u043d\u0435\u0439.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u041d\u0435 \u0441\u0442\u043e\u0438\u0442 \u043f\u0443\u0433\u0430\u0442\u044c\u0441\u044f, \u0447\u0442\u043e \u0432\u0438\u0434\u044b \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0437\u0430\u043f\u0438\u0441\u0430\u043d\u044b \u0447\u0435\u0440\u0435\u0437 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0412\u043c\u0435\u0441\u0442\u043e \\(f(x)\\) \u0438 \\(g(x)\\) \u043c\u043e\u0436\u0435\u0442 \u0441\u0442\u043e\u044f\u0442\u044c \u043b\u044e\u0431\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435!&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u0427\u0443\u0434\u043e-\u043c\u0435\u0442\u043e\u0434: \u043a\u0430\u043a \u043b\u0435\u0433\u043a\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u043b\u044e\u0431\u043e\u0435 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435?<\/strong><br><br>\u0422\u0430\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0440\u0435\u0448\u0430\u044e\u0442\u0441\u044f <strong>\u043c\u0435\u0442\u043e\u0434\u043e\u043c \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442<\/strong>. \u041e\u043d \u0437\u0430\u043a\u043b\u044e\u0447\u0430\u0435\u0442\u0441\u044f \u0432 \u0442\u0440\u0435\u0445 \u043f\u0440\u043e\u0441\u0442\u044b\u0445 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u044f\u0445:<br><br><strong>\u0428\u0430\u0433 1.<\/strong> \u0418\u0437\u043e\u043b\u0438\u0440\u0443\u0435\u043c \u043a\u043e\u0440\u0435\u043d\u044c \u0441 \u043e\u0434\u043d\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u043e\u0442 \u0437\u043d\u0430\u043a\u0430 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430, \u0442\u043e \u0435\u0441\u0442\u044c \u0441\u043b\u0435\u0432\u0430 \u043c\u044b \u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u0442\u043e\u043b\u044c\u043a\u043e \u043a\u043e\u0440\u0435\u043d\u044c.<br><strong>\u0428\u0430\u0433 2.<\/strong> \u041f\u0435\u0440\u0435\u043d\u043e\u0441\u0438\u043c \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u0432 \u0434\u0440\u0443\u0433\u0443\u044e \u0441\u0442\u043e\u0440\u043e\u043d\u0443.&nbsp;<br><strong>\u0428\u0430\u0433 3.<\/strong> \u0414\u0430\u043b\u0435\u0435 \u043d\u0443\u0436\u043d\u043e \u0432\u043e\u0437\u0432\u0435\u0441\u0442\u0438 \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f (\u0438 \u043f\u0440\u0430\u0432\u0443\u044e, \u0438 \u043b\u0435\u0432\u0443\u044e) \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442, \u0447\u0442\u043e\u0431\u044b \u0438\u0437\u0431\u0430\u0432\u0438\u0442\u044c\u0441\u044f \u043e\u0442 \u0437\u043d\u0430\u043a\u0430 \u043a\u043e\u0440\u043d\u044f.&nbsp;<br><br>\u0422\u0430\u043a\u043e\u0439 \u043c\u0435\u0442\u043e\u0434 \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0441\u0442\u043e\u043b\u044c\u043a\u043e \u0440\u0430\u0437, \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u043e\u0442\u0440\u0435\u0431\u0443\u0435\u0442\u0441\u044f, \u0447\u0442\u043e\u0431\u044b \u0438\u0437\u0431\u0430\u0432\u0438\u0442\u044c\u0441\u044f \u043e\u0442 \u0432\u0441\u0435\u0445 \u043a\u043e\u0440\u043d\u0435\u0439 \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u0427\u0442\u043e \u043d\u0443\u0436\u043d\u043e \u0443\u0447\u0438\u0442\u044b\u0432\u0430\u0442\u044c \u043f\u0440\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442? <strong>\u041a\u043e\u0440\u0435\u043d\u044c \u043d\u0435 \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u043c<\/strong>, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043d\u0443\u0436\u043d\u043e \u0434\u043e\u0431\u0430\u0432\u043b\u044f\u0442\u044c \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u043d\u0430 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u043a \u043a\u043e\u0442\u043e\u0440\u043e\u043c\u0443 \u043f\u0440\u0438\u0440\u0430\u0432\u043d\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u043a\u043e\u0440\u0435\u043d\u044c. \u0422\u0430\u043a\u043e\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 <strong>\u0432\u0441\u0435\u0433\u0434\u0430 \u0431\u043e\u043b\u044c\u0448\u0435 \u0438\u043b\u0438 \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u043b\u044e.<\/strong><\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\"><strong>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong><br><br>1. \u041f\u043e\u043c\u0435\u0441\u0442\u0438\u0442\u044c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0441 \u043a\u043e\u0440\u043d\u0435\u043c \u0432 \u043e\u0434\u043d\u0443 \u0447\u0430\u0441\u0442\u044c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u0430 \u0432\u0441\u0435 \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u043e\u0435 \u0432 \u0434\u0440\u0443\u0433\u0443\u044e.<br>2. \u0412\u043e\u0437\u0432\u0435\u0441\u0442\u0438 \u0432 \u043d\u0443\u0436\u043d\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f.<br>3. \u041f\u0435\u0440\u0432\u044b\u0435 \u0434\u0432\u0430 \u043f\u0443\u043d\u043a\u0442\u0430 \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u0432\u0442\u043e\u0440\u044f\u0442\u044c, \u043f\u043e\u043a\u0430 \u043d\u0435 \u0438\u0437\u0431\u0430\u0432\u0438\u0442\u0435\u0441\u044c \u043e\u0442 \u0432\u0441\u0435\u0445 \u043a\u043e\u0440\u043d\u0435\u0439.<br>4. \u0420\u0435\u0448\u0438\u0442\u044c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435.<\/p>\n\n\n\n<p>\u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0430.<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0432\u0438\u0434\u0430 \\(\\sqrt{f(x)}=g(x)\\):<\/strong><\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/3_logo.png\" alt=\"\" class=\"wp-image-23340\" width=\"294\" height=\"68\" srcset=\"\/library\/wp-content\/uploads\/2023\/02\/3_logo.png 587w, \/library\/wp-content\/uploads\/2023\/02\/3_logo-300x70.png 300w\" sizes=\"auto, (max-width: 294px) 100vw, 294px\" \/><\/figure><\/div>\n\n\n\n<p>\u041f\u0440\u0438\u043c\u0435\u0440:&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(\\sqrt{x^2-5}=x+1\\)<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\u041f\u0435\u0440\u0435\u0439\u0434\u0435\u043c \u043a \u0441\u0438\u0441\u0442\u0435\u043c\u0435. \u0412 \u043d\u0430\u0448\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \\(f(x)=x^2-5, g(x)=x+1\\).&nbsp;<\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/4_logo.png\" alt=\"\" class=\"wp-image-23341\" width=\"177\" height=\"63\" srcset=\"\/library\/wp-content\/uploads\/2023\/02\/4_logo.png 353w, \/library\/wp-content\/uploads\/2023\/02\/4_logo-300x107.png 300w\" sizes=\"auto, (max-width: 177px) 100vw, 177px\" \/><\/figure><\/div>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\"><li>\u0420\u0435\u0448\u0438\u043c \u043f\u0435\u0440\u0432\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \\(x^2-5=(x+1)^2\\).<\/li><\/ol>\n\n\n\n<p>\u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0441\u043a\u043e\u0431\u043a\u0438. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u0441\u043e\u043a\u0440\u0430\u0449\u0435\u043d\u043d\u043e\u0433\u043e \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0430 \u0441\u0443\u043c\u043c\u044b \\((a+b)^2=a^2+2ab+b^2\\):<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(x^2-5=x^2+2x+1\\).<\/p>\n\n\n\n<p>\u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \u0432\u0441\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u0432\u043b\u0435\u0432\u043e:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(x^2-5-x^2-2x-1=0\\)<br>\\(-2x-6=0\\)<br>\\(2x=-6\\)<\/p>\n\n\n\n<p>\u041f\u043e\u043b\u0443\u0447\u0438\u043c \\(x=-3\\), \u043d\u043e \u0434\u0430\u043d\u043d\u044b\u0439 \u043a\u043e\u0440\u0435\u043d\u044c \u043d\u0435 \u043f\u043e\u0434\u0445\u043e\u0434\u0438\u0442 \u043f\u043e\u0434 \u0432\u0442\u043e\u0440\u043e\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0435, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 <strong>\u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u043a\u043e\u0440\u043d\u0435\u0439.<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\"><li><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0432\u0438\u0434\u0430 \\(\\sqrt{f(x)}=\\sqrt{g(x)}\\):<\/strong><\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/5_logo-1024x76.png\" alt=\"\" class=\"wp-image-23344\" width=\"768\" height=\"57\" srcset=\"\/library\/wp-content\/uploads\/2023\/02\/5_logo-1024x76.png 1024w, \/library\/wp-content\/uploads\/2023\/02\/5_logo-300x22.png 300w, \/library\/wp-content\/uploads\/2023\/02\/5_logo-768x57.png 768w, \/library\/wp-content\/uploads\/2023\/02\/5_logo-1536x114.png 1536w, \/library\/wp-content\/uploads\/2023\/02\/5_logo.png 1873w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><\/figure><\/div>\n\n\n\n<p>\u041f\u0440\u0438\u043c\u0435\u0440:&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(\\sqrt{x^2+2}={2x+2}\\)<\/p>\n\n\n\n<p>\u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \\(f(x)=x^2+2, g(x)=2x+2\\).<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\u041f\u0435\u0440\u0435\u0439\u0434\u0435\u043c \u043a <a href=\"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/#\u0442\u0435\u0440\u043c\u0438\u043d\u044b\" target=\"_blank\" rel=\"noreferrer noopener\">\u0441\u0438\u0441\u0442\u0435\u043c\u0435<\/a>:\u00a0<\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/6_logo-1.png\" alt=\"\" class=\"wp-image-23346\" width=\"170\" height=\"67\" srcset=\"\/library\/wp-content\/uploads\/2023\/02\/6_logo-1.png 339w, \/library\/wp-content\/uploads\/2023\/02\/6_logo-1-300x119.png 300w\" sizes=\"auto, (max-width: 170px) 100vw, 170px\" \/><\/figure><\/div>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\"><li>\u0417\u0430\u043c\u0435\u0442\u0438\u043c, \u0447\u0442\u043e \u0432\u0442\u043e\u0440\u043e\u0435 \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u043f\u0440\u0438 \u043b\u044e\u0431\u043e\u043c <em>\u0445<\/em>:<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\">\\(x^2\\geq-2\\).<\/p>\n\n\n\n<p>\u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0447\u0438\u0441\u043b\u0430 \u2014 \u044d\u0442\u043e \u0432\u0441\u0435\u0433\u0434\u0430 \u043d\u0435\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u0442\u043e\u0433\u0434\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0447\u0438\u0441\u043b\u0430 \u0432\u0441\u0435\u0433\u0434\u0430 \u0431\u0443\u0434\u0435\u0442<strong> \u0431\u043e\u043b\u044c\u0448\u0435 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430<\/strong>. \u0417\u043d\u0430\u0447\u0438\u0442, \u0432\u0441\u0435 \u043a\u043e\u0440\u043d\u0438 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0431\u0443\u0434\u0443\u0442 \u044f\u0432\u043b\u044f\u0442\u044c\u0441\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u043c\u0438.&nbsp;<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\"><li>\u0420\u0435\u0448\u0438\u043c \u043d\u0435\u043f\u043e\u043b\u043d\u043e\u0435 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\">\\(x^2+2-2x-2=0\\)<br>\\(x^2-2x=0\\)<br>\\(x(x-2)=0\\)<br>\\(x=0\\) \u0438 \\(x-2=0\\).&nbsp;<\/p>\n\n\n\n<p>\u041f\u043e\u043b\u0443\u0447\u0438\u043c \u043a\u043e\u0440\u043d\u0438 0 \u0438 2.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\"><li><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441 \u0442\u0440\u0435\u043c\u044f \u043a\u043e\u0440\u043d\u044f\u043c\u0438:<\/strong><\/li><\/ol>\n\n\n\n<p>\u041f\u0440\u0438\u043c\u0435\u0440:&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(\\sqrt{1+x}-\\sqrt{1-x}=\\sqrt{x}\\)<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\u041d\u0430\u0439\u0434\u0435\u043c <strong>\u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0434\u043e\u043f\u0443\u0441\u0442\u0438\u043c\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439<\/strong> <strong>(\u041e\u0414\u0417)<\/strong>, \u0442\u043e \u0435\u0441\u0442\u044c \u0432\u0441\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 x \u043c\u043e\u0436\u0435\u0442 \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0442\u044c \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438 \u0438\u043b\u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0435.<\/li><\/ol>\n\n\n\n<p>\u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0441\u043e\u0441\u0442\u0430\u0432\u0438\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0443\u0441\u043b\u043e\u0432\u0438\u0439 \u043d\u0430 \u043f\u043e\u0434\u043a\u043e\u0440\u0435\u043d\u043d\u044b\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f, \u0430 \u043f\u043e\u0441\u043b\u0435 \u043d\u0430\u0439\u0434\u0435\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u044d\u0442\u043e\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u044b:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li><\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/7_logo-1.png\" alt=\"\" class=\"wp-image-23351\" width=\"104\" height=\"98\"\/><\/figure><\/div>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\"><li><\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/8_logo.png\" alt=\"\" class=\"wp-image-23352\" width=\"210\" height=\"88\" srcset=\"\/library\/wp-content\/uploads\/2023\/02\/8_logo.png 419w, \/library\/wp-content\/uploads\/2023\/02\/8_logo-300x126.png 300w\" sizes=\"auto, (max-width: 210px) 100vw, 210px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center\"> \\(0\u2264x\u22641\\)<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u0411\u0435\u0437 \u043a\u0430\u043a\u0438\u0445 \u0442\u0440\u0435\u0445 \u0431\u0443\u043a\u0432 \u043d\u0435 \u0441\u043f\u0440\u0430\u0432\u0438\u0442\u044c\u0441\u044f \u0441 \u0415\u0413\u042d?<\/strong><br><br>\u0422\u0430\u043a\u0438\u043c \u0442\u0440\u0435\u043c\u044f \u0431\u0443\u043a\u0432\u0430\u043c\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0430\u0431\u0431\u0440\u0435\u0432\u0438\u0430\u0442\u0443\u0440\u0430 \u041e\u0414\u0417.&nbsp;\u0412 \u0431\u0430\u0437\u043e\u0432\u043e\u043c \u0415\u0413\u042d \u0438 \u043f\u0435\u0440\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0438 \u043f\u0440\u043e\u0444\u0438\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u043c\u043e\u0436\u043d\u043e \u043e\u0431\u043e\u0439\u0442\u0438\u0441\u044c \u0438 \u0431\u0435\u0437 \u041e\u0414\u0417. \u041d\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0437\u0430\u0434\u0430\u043d\u0438\u044f \u0432\u0442\u043e\u0440\u043e\u0439 \u0447\u0430\u0441\u0442\u0438 \u043f\u0440\u043e\u0444\u0438\u043b\u044f \u0431\u0435\u0437 \u041e\u0414\u0417 \u043d\u0435 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u0441\u044f.<br><br>\u0427\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0432\u0435\u0440\u043d\u044b\u0439 \u043e\u0442\u0432\u0435\u0442, \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u043c \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0435\u043c \u043d\u0443\u0436\u043d\u043e \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u044c \u041e\u0414\u0417 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441 \u0435\u0433\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u043c\u0438. \u041f\u0440\u043e\u043c\u0435\u0436\u0443\u0442\u043a\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0431\u0443\u0434\u0443\u0442 \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0442\u044c \u0438 \u041e\u0414\u0417, \u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u044e, \u043f\u043e\u0439\u0434\u0443\u0442 \u0432 \u043e\u0442\u0432\u0435\u0442.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/14-13-733x1024.png\" alt=\"\" class=\"wp-image-23360\" width=\"367\" height=\"512\" srcset=\"\/library\/wp-content\/uploads\/2023\/02\/14-13-733x1024.png 733w, \/library\/wp-content\/uploads\/2023\/02\/14-13-215x300.png 215w, \/library\/wp-content\/uploads\/2023\/02\/14-13-768x1073.png 768w, \/library\/wp-content\/uploads\/2023\/02\/14-13-1100x1536.png 1100w, \/library\/wp-content\/uploads\/2023\/02\/14-13-1467x2048.png 1467w\" sizes=\"auto, (max-width: 367px) 100vw, 367px\" \/><\/figure><\/div>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\"><li>\u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \u043e\u0434\u043d\u043e \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0435 \u0432 \u043f\u0440\u0430\u0432\u0443\u044e \u0447\u0430\u0441\u0442\u044c:<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\">\\(\\sqrt{1+x}=\\sqrt{x}+\\sqrt{1-x}\\).<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\"><li>\u0412\u043e\u0437\u0432\u0435\u0434\u0435\u043c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442:<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\">\\((\\sqrt{1+x})^2=(\\sqrt{x}+\\sqrt{1-x})^2\\)<\/p>\n\n\n\n<p>\u0421\u043f\u0440\u0430\u0432\u0430 \u043e\u0442 \u0437\u043d\u0430\u043a\u0430 \u0440\u0430\u0432\u043d\u043e \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u0441\u043e\u043a\u0440\u0430\u0449\u0435\u043d\u043d\u043e\u0433\u043e \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \\((a+b)^2=a^2+2ab+b^2\\):&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(1+x=x+2*\\sqrt{x-1}*\\sqrt{x}+1-x\\).<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\"><li>\u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \u0432\u0441\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u0432 \u043e\u0434\u043d\u0443 \u0441\u0442\u043e\u0440\u043e\u043d\u0443 \u0438 \u0441\u043b\u043e\u0436\u0438\u043c <a href=\"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/#\u0442\u0435\u0440\u043c\u0438\u043d\u044b\" target=\"_blank\" rel=\"noreferrer noopener\">\u043f\u043e\u0434\u043e\u0431\u043d\u044b\u0435<\/a>:<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\">\\(1+x-x-2\\sqrt{x-1}*\\sqrt{x}-1+x=0\\)<br>\\(x-\\sqrt{x-1}*\\sqrt{x}=0\\)<\/p>\n\n\n\n<p>\u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \u0432\u0442\u043e\u0440\u043e\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0435 \u0432\u043f\u0440\u0430\u0432\u043e \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0432\u0438\u0434\u0430 \\(2\\sqrt{f(x)}=g(x)\\)<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(x=2\\sqrt{1-x}*\\sqrt{x}\\).<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\"><li>\u0421\u043d\u043e\u0432\u0430 \u043f\u0435\u0440\u0435\u0439\u0434\u0435\u043c \u043a \u0441\u0438\u0441\u0442\u0435\u043c\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439:<\/li><\/ol>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/9_logo.png\" alt=\"\" class=\"wp-image-23364\" width=\"145\" height=\"63\"\/><\/figure><\/div>\n\n\n\n<ol class=\"wp-block-list\" start=\"6\"><li>\u0420\u0435\u0448\u0438\u043c \u043f\u0435\u0440\u0432\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435. \u0414\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0440\u0430\u0441\u043a\u0440\u044b\u0442\u044c \u0441\u043a\u043e\u0431\u043a\u0438, \u043f\u0435\u0440\u0435\u043d\u0435\u0441\u0442\u0438 \u0432\u0441\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u0432 \u043e\u0434\u043d\u0443 \u0441\u0442\u043e\u0440\u043e\u043d\u0443, \u0441\u043b\u043e\u0436\u0438\u0442\u044c \u043f\u043e\u0434\u043e\u0431\u043d\u044b\u0435 \u0438 \u043d\u0430\u0439\u0442\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <em>\u0445<\/em>:&nbsp;<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center\">\\(x^2=4x(1-x)\\)<br>\\(x^2=4x-4x^2\\)<br>\\(x^2-4x+4x^2=0\\)<br>\\(5x^2-4x=0\\)<br>\\(x(5x-4)=0\\)<\/p>\n\n\n\n<p>\u0415\u0441\u043b\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043c\u043d\u043e\u0436\u0438\u0442\u0435\u043b\u0435\u0439 \u0440\u0430\u0432\u043d\u043e 0, \u0442\u043e \u043a\u0430\u0436\u0434\u044b\u0439 \u043c\u043d\u043e\u0436\u0438\u0442\u0435\u043b\u044c \u0440\u0430\u0432\u0435\u043d 0. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n\n\n\n<p class=\"has-text-align-left\">\\(x=0\\)<br>\\(5x-4=0 =&gt; x=\\frac{4}{5}\\).&nbsp;<\/p>\n\n\n\n<p>\u041e\u0431\u0430 \u043a\u043e\u0440\u043d\u044f \u043f\u043e\u0434\u0445\u043e\u0434\u044f\u0442 \u0438 \u043f\u043e\u0434 \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \\(x \u2265 0\\), \u0438 \u043f\u043e\u0434 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u043e\u0435 \u0440\u0430\u043d\u0435\u0435 \u041e\u0414\u0417, \u0437\u043d\u0430\u0447\u0438\u0442, \u043a\u043e\u0440\u043d\u0438 \u0434\u0430\u043d\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f 0 \u0438 \\(\\frac{4}{5}\\).<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\">\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044e\u0442\u0441\u044f \u043f\u043e\u0447\u0442\u0438 \u0432\u043e \u0432\u0441\u0435\u0445 \u0437\u0430\u0434\u0430\u043d\u0438\u044f\u0445 \u044d\u043a\u0437\u0430\u043c\u0435\u043d\u0430, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0441 \u0438\u0445 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043c\u043e\u0434\u0435\u043b\u0438, \u0440\u0435\u0448\u0430\u044e\u0442\u0441\u044f \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0438 \u0441\u0442\u0435\u0440\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438, \u043d\u0430\u0445\u043e\u0434\u044f\u0442\u0441\u044f \u043d\u0443\u043b\u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432 \u0438 \u043c\u043d\u043e\u0433\u043e\u0435-\u043c\u043d\u043e\u0433\u043e\u0435 \u0434\u0440\u0443\u0433\u043e\u0435. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0434\u043b\u044f \u0443\u0441\u043f\u0435\u0448\u043d\u043e\u0439 \u0441\u0434\u0430\u0447\u0438 \u044d\u043a\u0437\u0430\u043c\u0435\u043d\u0430 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0443\u043c\u0435\u0442\u044c \u0440\u0435\u0448\u0430\u0442\u044c \u043b\u044e\u0431\u043e\u0439 \u0432\u0438\u0434 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439.<br><br>\u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u043e\u0442\u0434\u0435\u043b\u044c\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u043d\u0438\u044f, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, <strong>\u0432 \u043f\u0440\u043e\u0444\u0438\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u044d\u0442\u043e \u043d\u043e\u043c\u0435\u0440\u0430 5 \u0438 12, \u0432 \u0431\u0430\u0437\u043e\u0432\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u2014 \u211617, \u0430 \u0432 \u041e\u0413\u042d \u2014 \u21169 \u0438 \u211620.&nbsp;<\/strong><\/p>\n\n\n\n<p>\u0414\u043b\u044f \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u0440\u0430\u0437\u0431\u0435\u0440\u0435\u043c <strong>\u211612 \u0438\u0437 \u0415\u0413\u042d \u043f\u043e \u043f\u0440\u043e\u0444\u0438\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435.<\/strong>&nbsp;<\/p>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435.&nbsp;<\/strong><\/p>\n\n\n\n<p><em>\u0430) \u0420\u0435\u0448\u0438\u0442\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435: <\/em>\\(y-\\sqrt{78-2y}+1=0\\).<\/p>\n\n\n\n<p><em>\u0431) \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043a\u043e\u0440\u043d\u0438 \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0449\u0438\u0435 \u043e\u0442\u0440\u0435\u0437\u043a\u0443 <\/em>\\((\\sqrt{37};\\sqrt{53})\\)<em>.<\/em><\/p>\n\n\n\n<p><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435.&nbsp;<\/strong><\/p>\n\n\n\n<p>\u0430) \u041e\u0441\u0442\u0430\u0432\u0438\u043c \u043a\u043e\u0440\u0435\u043d\u044c \u0441\u043b\u0435\u0432\u0430, \u0430 \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u043f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \u0432\u043f\u0440\u0430\u0432\u043e:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(\\sqrt{78-2y}=y+1\\)<\/p>\n\n\n\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u043e\u0439:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/3_logo-1.png\" alt=\"\" class=\"wp-image-23368\" width=\"294\" height=\"68\" srcset=\"\/library\/wp-content\/uploads\/2023\/02\/3_logo-1.png 587w, \/library\/wp-content\/uploads\/2023\/02\/3_logo-1-300x70.png 300w\" sizes=\"auto, (max-width: 294px) 100vw, 294px\" \/><\/figure><\/div>\n\n\n\n<p>, \u0433\u0434\u0435 \\(f(x)=\\sqrt{78-2y}, g(x)=y+1\\)<\/p>\n\n\n\n<p>\u0420\u0435\u0448\u0438\u043c \u0432\u0442\u043e\u0440\u043e\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0438\u0437 \u0441\u0438\u0441\u0442\u0435\u043c\u044b:<br>\\(y+1\\geq 0\\)<br>\\(y\\geq -1\\) \u2014 \u044d\u0442\u043e \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u0435 \u043d\u0430 \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0435 \u043a\u043e\u0440\u043d\u0438, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043d\u0443\u0436\u043d\u043e \u0431\u0443\u0434\u0435\u0442 \u0443\u0447\u0435\u0441\u0442\u044c \u0432 \u043a\u043e\u043d\u0446\u0435.&nbsp;<\/p>\n\n\n\n<p>\u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u0440\u0435\u0448\u0438\u043c \u0441\u0430\u043c\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(78-2y=(y+1)^2\\)<\/p>\n\n\n\n<p>\u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0441\u043a\u043e\u0431\u043a\u0438, \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c\u0441\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u043e\u0439 \u0441\u043e\u043a\u0440\u0430\u0449\u0435\u043d\u043d\u043e\u0433\u043e \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \\((a+b)^2=a^2+2ab+b^2\\). \u041f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(78-2y=y^2+2y+1\\)<\/p>\n\n\n\n<p>\u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \u0432\u0441\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u0432 \u043e\u0434\u043d\u0443 \u0441\u0442\u043e\u0440\u043e\u043d\u0443 \u0438 \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043c \u043f\u043e\u0434\u043e\u0431\u043d\u044b\u0435:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(y^2+2y+1-78+2y=0\\)<br>\\(y^2+4y-77=0\\)<\/p>\n\n\n\n<p>\u0420\u0435\u0448\u0438\u043c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0434\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043c\u044b \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043b\u0438 \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 \u00ab<a href=\"https:\/\/umschool.net\/library\/matematika\/linejnye-kvadratnye-i-kubicheskie-uravneniya-2\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u041b\u0438\u043d\u0435\u0439\u043d\u044b\u0435, \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0435 \u0438 \u043a\u0443\u0431\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/a>\u00bb:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(D=b^2-4ac=4^2-4*(-77)=16+308=324\\)<br>\\(y_1=\\frac{-b+\\sqrt{D}}{2a}=\\frac{-4+18}{2}=7\\)<br>\\(y_2=\\frac{-b-\\sqrt{D}}{2a}=\\frac{-4-18}{2}=-11\\)<\/p>\n\n\n\n<p>\u0412\u0441\u043f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u043e\u0433\u0440\u0430\u043d\u0438\u0447\u0435\u043d\u0438\u0435 \\(y\\geq -1\\). \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043d\u0430\u043c \u043f\u043e\u0434\u0445\u043e\u0434\u0438\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u043a\u043e\u0440\u0435\u043d\u044c \\(y=7\\).&nbsp;<\/p>\n\n\n\n<p>\u0431) \u041f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u043c \\(7\\) \u0432 \u0432\u0438\u0434\u0435 \u043a\u043e\u0440\u043d\u044f, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \\(\\sqrt{49}\\).&nbsp;<\/p>\n\n\n\n<p>\u0417\u0430\u043c\u0435\u0442\u0438\u043c, \u0447\u0442\u043e \\(\\sqrt{37}&lt;\\sqrt{49}&lt;\\sqrt{53}\\), \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \\(y=7\\) \u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0438\u0442 \u043e\u0442\u0440\u0435\u0437\u043a\u0443 \\((\\sqrt{37};\\sqrt{53})\\).&nbsp;<\/p>\n\n\n\n<p><strong>\u041e\u0442\u0432\u0435\u0442: <\/strong>\u0430) 7; \u0431) 7.&nbsp;&nbsp;<\/p>\n\n\n\n<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0438\u0437\u0443\u0447\u0438\u043b\u0438 \u0446\u0435\u043b\u044b\u0445 \u0442\u0440\u0438 \u0432\u0438\u0434\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439. \u041d\u043e \u043d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435 \u0438\u0445 \u0437\u043d\u0430\u0447\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0431\u043e\u043b\u044c\u0448\u0435! \u0418 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u044d\u0442\u0430\u043f \u2014 <a href=\"https:\/\/umschool.net\/library\/matematika\/pokazatelnye-uravneniya-i-neravenstva\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/a>.&nbsp;<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u0442\u0435\u0440\u043c\u0438\u043d\u044b\"><strong>\u0422\u0435\u0440\u043c\u0438\u043d\u044b<\/strong><\/h2>\n\n\n\n<p><strong>\u041f\u043e\u0434\u043e\u0431\u043d\u044b\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 <\/strong>\u2014 \u044d\u0442\u043e \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0438\u043c\u0435\u044e\u0442 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u0443\u044e \u0431\u0443\u043a\u0432\u0435\u043d\u043d\u0443\u044e \u0447\u0430\u0441\u0442\u044c, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043d\u0435 \u0438\u043c\u0435\u044e\u0442 \u0431\u0443\u043a\u0432\u0435\u043d\u043d\u043e\u0439 \u0447\u0430\u0441\u0442\u0438.<\/p>\n\n\n\n<p><strong>\u0421\u0438\u0441\u0442\u0435\u043c\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439<\/strong> \u2014 \u044d\u0442\u043e \u0434\u0432\u0430 \u0438 \u0431\u043e\u043b\u0435\u0435 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430, \u043e\u0431\u044a\u0435\u0434\u0438\u043d\u0435\u043d\u043d\u044b\u0445 \u0444\u0438\u0433\u0443\u0440\u043d\u043e\u0439 \u0441\u043a\u043e\u0431\u043a\u043e\u0439, \u0438\u043c\u0435\u044e\u0449\u0438\u0445 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0439, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043e\u0434\u043d\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u043e \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u043c\u0438 \u0434\u043b\u044f \u0432\u0441\u0435\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u044b.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u0424\u0430\u043a\u0442\u0447\u0435\u043a<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>\u0420\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> \u2014 \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0435\u0441\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0435, \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435, \u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438 \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0446\u0435\u043b\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c. \u0420\u0435\u0448\u0430\u0435\u0442\u0441\u044f \u0442\u0430\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0443\u0442\u0435\u043c \u0441\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043a \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u043e\u043c\u0443 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e, \u0442\u043e \u0435\u0441\u0442\u044c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0435\u0441\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u0435, \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u0435, \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435, \u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u0438\u043b\u0438 \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432 \u0446\u0435\u043b\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c.<\/li><li><strong>\u0414\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> \u2014 \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0443 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0445\u043e\u0442\u044f \u0431\u044b \u0432 \u043e\u0434\u043d\u043e\u0439 \u0434\u0440\u043e\u0431\u0438 \u0432 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435 \u0435\u0441\u0442\u044c \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0430\u044f. \u0414\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0443\u0436\u043d\u043e \u043f\u0440\u0438\u0432\u0435\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043a \u0432\u0438\u0434\u0443, \u043a\u043e\u0433\u0434\u0430 \u0434\u0440\u043e\u0431\u044c \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e, \u0438 \u043f\u0435\u0440\u0435\u0439\u0442\u0438 \u043a \u0441\u0438\u0441\u0442\u0435\u043c\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u0433\u0434\u0435 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u044c \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e, \u0430 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u044c \u2014 \u043d\u0435\u0442.<\/li><li>\u0412 <strong>\u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438<\/strong> \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0430\u044f \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442\u0441\u044f \u043f\u043e\u0434 \u043a\u043e\u0440\u043d\u0435\u043c \u0438\u043b\u0438 \u0432\u043e\u0437\u0432\u0435\u0434\u0435\u043d\u0430 \u0432 \u0434\u0440\u043e\u0431\u043d\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c. \u0414\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0440\u0430\u0432\u043d\u043e\u0441\u0438\u043b\u044c\u043d\u044b\u0435 \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u044b:<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/02\/11_logo-1-1-1024x118.png\" alt=\"\" class=\"wp-image-23372\" width=\"512\" height=\"59\" srcset=\"\/library\/wp-content\/uploads\/2023\/02\/11_logo-1-1-1024x118.png 1024w, \/library\/wp-content\/uploads\/2023\/02\/11_logo-1-1-300x34.png 300w, \/library\/wp-content\/uploads\/2023\/02\/11_logo-1-1-768x88.png 768w, \/library\/wp-content\/uploads\/2023\/02\/11_logo-1-1.png 1253w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li>&nbsp;\u0415\u0441\u043b\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 <strong>\u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u0438 \u043a\u043e\u0440\u043d\u0435\u0439<\/strong>, \u0442\u043e \u043c\u043e\u0436\u043d\u043e \u043a\u0430\u0436\u0434\u044b\u0439 \u0440\u0430\u0437 \u0432\u043e\u0437\u0432\u043e\u0434\u0438\u0442\u044c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0432 \u0441\u0442\u0435\u043f\u0435\u043d\u044c, \u043f\u043e\u043a\u0430 \u043d\u0435 \u0438\u0437\u0431\u0430\u0432\u0438\u0442\u0435\u0441\u044c \u043e\u0442 \u043a\u043e\u0440\u043d\u0435\u0439. \u0422\u0430\u043a\u0436\u0435 \u043d\u0435 \u0441\u0442\u043e\u0438\u0442 \u0437\u0430\u0431\u044b\u0432\u0430\u0442\u044c \u043f\u0440\u043e \u041e\u0414\u0417.<\/li><\/ul>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u041f\u0440\u043e\u0432\u0435\u0440\u044c \u0441\u0435\u0431\u044f<\/strong><\/h2>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 1.<\/strong><br>\u0412\u044b\u0431\u0435\u0440\u0438\u0442\u0435 \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(\\frac{x^2+2x+3}{3}=2x+1\\)<\/li><li>\\(x^3+2x=0\\)<\/li><li>\\(\\frac{x^2+1}{x-3}=0\\)<\/li><li>\\(\\sqrt{x-2}=\\sqrt{x^3-8}\\)<\/li><\/ol>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 2.<\/strong><br>\u0412\u044b\u0431\u0435\u0440\u0438\u0442\u0435 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\((x-2)(3x+1)=0\\)<\/li><li>\\(\\sqrt{x}-2=-x\\)<\/li><li>\\(5x^2+8x-1=3^2\\)<\/li><li>\\(\\frac{x+7}{2x}=5\\)<\/li><\/ol>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 3.<\/strong><br>\u0420\u0435\u0448\u0438\u0442\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \\(\\frac{5x+2}{3}=x\\).<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>-1<\/li><li>2<\/li><li>-2<\/li><li>3<\/li><\/ol>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 4.<\/strong><br>\u0420\u0435\u0448\u0438\u0442\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \\(\\frac{9x-15}{x-5}=\\frac{1}{x-3}\\).<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(2\\) \u0438 \\(\\frac{25}{9}\\)<\/li><li>\\(-2\\) \u0438 \\(\\frac{9}{25}\\)<\/li><li>\\(9\\) \u0438 \\(25\\)<\/li><li>\\(\\frac{25}{9}\\) \u0438 \\(-2\\)<\/li><\/ol>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 5.<\/strong><br>\u0420\u0435\u0448\u0438\u0442\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \\(\\sqrt{x^2+3x}=\\sqrt{5x-1}\\).<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>1 \u0438 2<\/li><li>1<\/li><li>0 \u0438 2<\/li><li>2<\/li><\/ol>\n\n\n\n<p><strong>\u041e\u0442\u0432\u0435\u0442\u044b: 1.<\/strong> \u2014 3; <strong>2.<\/strong> \u2014 2; <strong>3.<\/strong> \u2014 1; <strong>4.<\/strong> \u2014 1; <strong>5.<\/strong> \u2014 2.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435 \u041a\u0430\u043a \u043d\u0435 \u043f\u0435\u0440\u0435\u043f\u0443\u0442\u0430\u0442\u044c \u0446\u0435\u043b\u043e\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0441 \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435\u043c? \u0427\u0443\u0434\u043e-\u043c\u0435\u0442\u043e\u0434: \u043a\u0430\u043a \u043b\u0435\u0433\u043a\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u043b\u044e\u0431\u043e\u0435 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435? \u0411\u0435\u0437 \u043a\u0430\u043a\u0438\u0445 \u0442\u0440\u0435\u0445 \u0431\u0443\u043a\u0432 \u043d\u0435 \u0441\u043f\u0440\u0430\u0432\u0438\u0442\u044c\u0441\u044f \u0441 \u0415\u0413\u042d? \u0421\u0440\u0430\u0432\u043d\u0438\u0442\u044c \u0437\u0430\u0440\u043f\u043b\u0430\u0442\u0443 \u0438 \u0440\u0430\u0441\u0445\u043e\u0434\u044b, \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u043e\u0432 \u0432 \u0431\u043b\u044e\u0434\u0435 \u0438\u043b\u0438 \u0440\u0435\u0448\u0438\u0442\u044c, \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u043b\u0438\u0442\u043a\u0438 \u0432\u0437\u044f\u0442\u044c \u0434\u043b\u044f \u0440\u0435\u043c\u043e\u043d\u0442\u0430 \u0432 \u0432\u0430\u043d\u043d\u043e\u0439 \u2014 \u043c\u044b \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0433\u043e\u0440\u0430\u0437\u0434\u043e \u0447\u0430\u0449\u0435, \u0447\u0435\u043c \u043a\u0430\u0436\u0435\u0442\u0441\u044f. \u0412 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":6152,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[27,102],"class_list":["post-4344","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-matematika","tag-uravneniya"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f - \u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a<\/title>\n<meta name=\"description\" content=\"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. \u0412\u0441\u0435 \u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u043f\u043e\u043d\u044f\u0442\u043d\u044b\u043c \u044f\u0437\u044b\u043a\u043e\u043c. \u041b\u0443\u0447\u0448\u0438\u0435 \u0443\u0447\u0435\u0431\u043d\u044b\u0435 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u044b \u0434\u043b\u044f \u0448\u043a\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432 \u0438 \u0432\u0437\u0440\u043e\u0441\u043b\u044b\u0445 \u043e\u0442 \u043e\u043d\u043b\u0430\u0439\u043d-\u0448\u043a\u043e\u043b\u044b \u0423\u043c\u0441\u043a\u0443\u043b.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f - \u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a\" \/>\n<meta property=\"og:description\" content=\"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. \u0412\u0441\u0435 \u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u043f\u043e\u043d\u044f\u0442\u043d\u044b\u043c \u044f\u0437\u044b\u043a\u043e\u043c. \u041b\u0443\u0447\u0448\u0438\u0435 \u0443\u0447\u0435\u0431\u043d\u044b\u0435 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u044b \u0434\u043b\u044f \u0448\u043a\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432 \u0438 \u0432\u0437\u0440\u043e\u0441\u043b\u044b\u0445 \u043e\u0442 \u043e\u043d\u043b\u0430\u0439\u043d-\u0448\u043a\u043e\u043b\u044b \u0423\u043c\u0441\u043a\u0443\u043b.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a\" \/>\n<meta property=\"article:published_time\" content=\"2022-04-06T10:11:39+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-02-28T15:58:43+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/umschool.net\/library\/wp-content\/uploads\/2022\/04\/raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1874\" \/>\n\t<meta property=\"og:image:height\" content=\"1056\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"umschool\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u041d\u0430\u043f\u0438\u0441\u0430\u043d\u043e \u0430\u0432\u0442\u043e\u0440\u043e\u043c\" \/>\n\t<meta name=\"twitter:data1\" content=\"umschool\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u041f\u0440\u0438\u043c\u0435\u0440\u043d\u043e\u0435 \u0432\u0440\u0435\u043c\u044f \u0434\u043b\u044f \u0447\u0442\u0435\u043d\u0438\u044f\" \/>\n\t<meta name=\"twitter:data2\" content=\"12 \u043c\u0438\u043d\u0443\u0442\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\n\t    \"@context\": \"https:\\\/\\\/schema.org\",\n\t    \"@graph\": [\n\t        {\n\t            \"@type\": \"Article\",\n\t            \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/matematika\\\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\\\/#article\",\n\t            \"isPartOf\": {\n\t                \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/matematika\\\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\\\/\"\n\t            },\n\t            \"author\": {\n\t                \"name\": \"umschool\",\n\t                \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/#\\\/schema\\\/person\\\/279fc031eb415325d4fa22462381fbd6\"\n\t            },\n\t            \"headline\": \"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\",\n\t            \"datePublished\": \"2022-04-06T10:11:39+00:00\",\n\t            \"dateModified\": \"2023-02-28T15:58:43+00:00\",\n\t            \"mainEntityOfPage\": {\n\t                \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/matematika\\\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\\\/\"\n\t            },\n\t            \"wordCount\": 2152,\n\t            \"commentCount\": 0,\n\t            \"publisher\": {\n\t                \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/#organization\"\n\t            },\n\t            \"image\": {\n\t                \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/matematika\\\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\\\/#primaryimage\"\n\t            },\n\t            \"thumbnailUrl\": \"\\\/library\\\/wp-content\\\/uploads\\\/2022\\\/04\\\/raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya.png\",\n\t            \"keywords\": [\n\t                \"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\",\n\t                \"\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\"\n\t            ],\n\t            \"articleSection\": [\n\t                \"\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\"\n\t            ],\n\t            \"inLanguage\": \"ru-RU\",\n\t            \"potentialAction\": [\n\t                {\n\t                    \"@type\": \"CommentAction\",\n\t                    \"name\": \"Comment\",\n\t                    \"target\": [\n\t                        \"https:\\\/\\\/umschool.net\\\/library\\\/matematika\\\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\\\/#respond\"\n\t                    ]\n\t                }\n\t            ]\n\t        },\n\t        {\n\t            \"@type\": \"WebPage\",\n\t            \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/matematika\\\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\\\/\",\n\t            \"url\": \"https:\\\/\\\/umschool.net\\\/library\\\/matematika\\\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\\\/\",\n\t            \"name\": \"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f - \u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a\",\n\t            \"isPartOf\": {\n\t                \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/#website\"\n\t            },\n\t            \"primaryImageOfPage\": {\n\t                \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/matematika\\\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\\\/#primaryimage\"\n\t            },\n\t            \"image\": {\n\t                \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/matematika\\\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\\\/#primaryimage\"\n\t            },\n\t            \"thumbnailUrl\": \"\\\/library\\\/wp-content\\\/uploads\\\/2022\\\/04\\\/raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya.png\",\n\t            \"datePublished\": \"2022-04-06T10:11:39+00:00\",\n\t            \"dateModified\": \"2023-02-28T15:58:43+00:00\",\n\t            \"description\": \"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. \u0412\u0441\u0435 \u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u043f\u043e\u043d\u044f\u0442\u043d\u044b\u043c \u044f\u0437\u044b\u043a\u043e\u043c. \u041b\u0443\u0447\u0448\u0438\u0435 \u0443\u0447\u0435\u0431\u043d\u044b\u0435 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u044b \u0434\u043b\u044f \u0448\u043a\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432 \u0438 \u0432\u0437\u0440\u043e\u0441\u043b\u044b\u0445 \u043e\u0442 \u043e\u043d\u043b\u0430\u0439\u043d-\u0448\u043a\u043e\u043b\u044b \u0423\u043c\u0441\u043a\u0443\u043b.\",\n\t            \"breadcrumb\": {\n\t                \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/matematika\\\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\\\/#breadcrumb\"\n\t            },\n\t            \"inLanguage\": \"ru-RU\",\n\t            \"potentialAction\": [\n\t                {\n\t                    \"@type\": \"ReadAction\",\n\t                    \"target\": [\n\t                        \"https:\\\/\\\/umschool.net\\\/library\\\/matematika\\\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\\\/\"\n\t                    ]\n\t                }\n\t            ]\n\t        },\n\t        {\n\t            \"@type\": \"ImageObject\",\n\t            \"inLanguage\": \"ru-RU\",\n\t            \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/matematika\\\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\\\/#primaryimage\",\n\t            \"url\": \"\\\/library\\\/wp-content\\\/uploads\\\/2022\\\/04\\\/raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya.png\",\n\t            \"contentUrl\": \"\\\/library\\\/wp-content\\\/uploads\\\/2022\\\/04\\\/raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya.png\",\n\t            \"width\": 1874,\n\t            \"height\": 1056\n\t        },\n\t        {\n\t            \"@type\": \"BreadcrumbList\",\n\t            \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/matematika\\\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\\\/#breadcrumb\",\n\t            \"itemListElement\": [\n\t                {\n\t                    \"@type\": \"ListItem\",\n\t                    \"position\": 1,\n\t                    \"name\": \"\u0413\u043b\u0430\u0432\u043d\u0430\u044f \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0430\",\n\t                    \"item\": \"https:\\\/\\\/umschool.net\\\/library\\\/\"\n\t                },\n\t                {\n\t                    \"@type\": \"ListItem\",\n\t                    \"position\": 2,\n\t                    \"name\": \"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\"\n\t                }\n\t            ]\n\t        },\n\t        {\n\t            \"@type\": \"WebSite\",\n\t            \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/#website\",\n\t            \"url\": \"https:\\\/\\\/umschool.net\\\/library\\\/\",\n\t            \"name\": \"\u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a\",\n\t            \"description\": \"\u041d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u043f\u043e\u043b\u043d\u0430\u044f \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044f \u043f\u0440\u043e \u0448\u043a\u043e\u043b\u044c\u043d\u044b\u0435 \u044d\u043a\u0437\u0430\u043c\u0435\u043d\u044b, \u043f\u043e\u0441\u0442\u0443\u043f\u043b\u0435\u043d\u0438\u0435 \u0432 \u0412\u0423\u0417\u044b \u0438 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u044b \u043e\u0442 \u043e\u043d\u043b\u0430\u0439\u043d-\u0448\u043a\u043e\u043b\u044b \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0438 \u043a \u0415\u0413\u042d \u0438 \u041e\u0413\u042d\",\n\t            \"publisher\": {\n\t                \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/#organization\"\n\t            },\n\t            \"potentialAction\": [\n\t                {\n\t                    \"@type\": \"SearchAction\",\n\t                    \"target\": {\n\t                        \"@type\": \"EntryPoint\",\n\t                        \"urlTemplate\": \"https:\\\/\\\/umschool.net\\\/library\\\/?s={search_term_string}\"\n\t                    },\n\t                    \"query-input\": {\n\t                        \"@type\": \"PropertyValueSpecification\",\n\t                        \"valueRequired\": true,\n\t                        \"valueName\": \"search_term_string\"\n\t                    }\n\t                }\n\t            ],\n\t            \"inLanguage\": \"ru-RU\"\n\t        },\n\t        {\n\t            \"@type\": \"Organization\",\n\t            \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/#organization\",\n\t            \"name\": \"\u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a\",\n\t            \"url\": \"https:\\\/\\\/umschool.net\\\/library\\\/\",\n\t            \"logo\": {\n\t                \"@type\": \"ImageObject\",\n\t                \"inLanguage\": \"ru-RU\",\n\t                \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/#\\\/schema\\\/logo\\\/image\\\/\",\n\t                \"url\": \"\\\/library\\\/wp-content\\\/uploads\\\/2021\\\/06\\\/umlogo.svg\",\n\t                \"contentUrl\": \"\\\/library\\\/wp-content\\\/uploads\\\/2021\\\/06\\\/umlogo.svg\",\n\t                \"width\": 191,\n\t                \"height\": 48,\n\t                \"caption\": \"\u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a\"\n\t            },\n\t            \"image\": {\n\t                \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/#\\\/schema\\\/logo\\\/image\\\/\"\n\t            }\n\t        },\n\t        {\n\t            \"@type\": \"Person\",\n\t            \"@id\": \"https:\\\/\\\/umschool.net\\\/library\\\/#\\\/schema\\\/person\\\/279fc031eb415325d4fa22462381fbd6\",\n\t            \"name\": \"umschool\",\n\t            \"image\": {\n\t                \"@type\": \"ImageObject\",\n\t                \"inLanguage\": \"ru-RU\",\n\t                \"@id\": \"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/1e8360de1e5c6968c838aa8f62f7fae7faec4111a33db284b5f8d4ce2022cb11?s=96&d=mm&r=g\",\n\t                \"url\": \"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/1e8360de1e5c6968c838aa8f62f7fae7faec4111a33db284b5f8d4ce2022cb11?s=96&d=mm&r=g\",\n\t                \"contentUrl\": \"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/1e8360de1e5c6968c838aa8f62f7fae7faec4111a33db284b5f8d4ce2022cb11?s=96&d=mm&r=g\",\n\t                \"caption\": \"umschool\"\n\t            },\n\t            \"sameAs\": [\n\t                \"http:\\\/\\\/umschool.frontendie.ru\"\n\t            ],\n\t            \"url\": \"https:\\\/\\\/umschool.net\\\/library\\\/author\\\/umschool\\\/\"\n\t        }\n\t    ]\n\t}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f - \u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a","description":"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. \u0412\u0441\u0435 \u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u043f\u043e\u043d\u044f\u0442\u043d\u044b\u043c \u044f\u0437\u044b\u043a\u043e\u043c. \u041b\u0443\u0447\u0448\u0438\u0435 \u0443\u0447\u0435\u0431\u043d\u044b\u0435 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u044b \u0434\u043b\u044f \u0448\u043a\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432 \u0438 \u0432\u0437\u0440\u043e\u0441\u043b\u044b\u0445 \u043e\u0442 \u043e\u043d\u043b\u0430\u0439\u043d-\u0448\u043a\u043e\u043b\u044b \u0423\u043c\u0441\u043a\u0443\u043b.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/","og_locale":"ru_RU","og_type":"article","og_title":"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f - \u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a","og_description":"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. \u0412\u0441\u0435 \u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u043f\u043e\u043d\u044f\u0442\u043d\u044b\u043c \u044f\u0437\u044b\u043a\u043e\u043c. \u041b\u0443\u0447\u0448\u0438\u0435 \u0443\u0447\u0435\u0431\u043d\u044b\u0435 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u044b \u0434\u043b\u044f \u0448\u043a\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432 \u0438 \u0432\u0437\u0440\u043e\u0441\u043b\u044b\u0445 \u043e\u0442 \u043e\u043d\u043b\u0430\u0439\u043d-\u0448\u043a\u043e\u043b\u044b \u0423\u043c\u0441\u043a\u0443\u043b.","og_url":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/","og_site_name":"\u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a","article_published_time":"2022-04-06T10:11:39+00:00","article_modified_time":"2023-02-28T15:58:43+00:00","og_image":[{"width":1874,"height":1056,"url":"https:\/\/umschool.net\/library\/wp-content\/uploads\/2022\/04\/raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya.png","type":"image\/png"}],"author":"umschool","twitter_card":"summary_large_image","twitter_misc":{"\u041d\u0430\u043f\u0438\u0441\u0430\u043d\u043e \u0430\u0432\u0442\u043e\u0440\u043e\u043c":"umschool","\u041f\u0440\u0438\u043c\u0435\u0440\u043d\u043e\u0435 \u0432\u0440\u0435\u043c\u044f \u0434\u043b\u044f \u0447\u0442\u0435\u043d\u0438\u044f":"12 \u043c\u0438\u043d\u0443\u0442"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/#article","isPartOf":{"@id":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/"},"author":{"name":"umschool","@id":"https:\/\/umschool.net\/library\/#\/schema\/person\/279fc031eb415325d4fa22462381fbd6"},"headline":"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f","datePublished":"2022-04-06T10:11:39+00:00","dateModified":"2023-02-28T15:58:43+00:00","mainEntityOfPage":{"@id":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/"},"wordCount":2152,"commentCount":0,"publisher":{"@id":"https:\/\/umschool.net\/library\/#organization"},"image":{"@id":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/#primaryimage"},"thumbnailUrl":"\/library\/wp-content\/uploads\/2022\/04\/raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya.png","keywords":["\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430","\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f"],"articleSection":["\u041c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430"],"inLanguage":"ru-RU","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/","url":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/","name":"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f - \u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a","isPartOf":{"@id":"https:\/\/umschool.net\/library\/#website"},"primaryImageOfPage":{"@id":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/#primaryimage"},"image":{"@id":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/#primaryimage"},"thumbnailUrl":"\/library\/wp-content\/uploads\/2022\/04\/raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya.png","datePublished":"2022-04-06T10:11:39+00:00","dateModified":"2023-02-28T15:58:43+00:00","description":"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f. \u0412\u0441\u0435 \u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u043f\u043e\u043d\u044f\u0442\u043d\u044b\u043c \u044f\u0437\u044b\u043a\u043e\u043c. \u041b\u0443\u0447\u0448\u0438\u0435 \u0443\u0447\u0435\u0431\u043d\u044b\u0435 \u043c\u0430\u0442\u0435\u0440\u0438\u0430\u043b\u044b \u0434\u043b\u044f \u0448\u043a\u043e\u043b\u044c\u043d\u0438\u043a\u043e\u0432 \u0438 \u0432\u0437\u0440\u043e\u0441\u043b\u044b\u0445 \u043e\u0442 \u043e\u043d\u043b\u0430\u0439\u043d-\u0448\u043a\u043e\u043b\u044b \u0423\u043c\u0441\u043a\u0443\u043b.","breadcrumb":{"@id":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/#breadcrumb"},"inLanguage":"ru-RU","potentialAction":[{"@type":"ReadAction","target":["https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/"]}]},{"@type":"ImageObject","inLanguage":"ru-RU","@id":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/#primaryimage","url":"\/library\/wp-content\/uploads\/2022\/04\/raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya.png","contentUrl":"\/library\/wp-content\/uploads\/2022\/04\/raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya.png","width":1874,"height":1056},{"@type":"BreadcrumbList","@id":"https:\/\/umschool.net\/library\/matematika\/czelye-raczionalnye-drobno-raczionalnye-i-irraczionalnye-uravneniya\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u0413\u043b\u0430\u0432\u043d\u0430\u044f \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0430","item":"https:\/\/umschool.net\/library\/"},{"@type":"ListItem","position":2,"name":"\u0426\u0435\u043b\u044b\u0435 \u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435, \u0434\u0440\u043e\u0431\u043d\u043e-\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0438 \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f"}]},{"@type":"WebSite","@id":"https:\/\/umschool.net\/library\/#website","url":"https:\/\/umschool.net\/library\/","name":"\u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a","description":"\u041d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u043f\u043e\u043b\u043d\u0430\u044f \u0438\u043d\u0444\u043e\u0440\u043c\u0430\u0446\u0438\u044f \u043f\u0440\u043e \u0448\u043a\u043e\u043b\u044c\u043d\u044b\u0435 \u044d\u043a\u0437\u0430\u043c\u0435\u043d\u044b, \u043f\u043e\u0441\u0442\u0443\u043f\u043b\u0435\u043d\u0438\u0435 \u0432 \u0412\u0423\u0417\u044b \u0438 \u043e\u043b\u0438\u043c\u043f\u0438\u0430\u0434\u044b \u043e\u0442 \u043e\u043d\u043b\u0430\u0439\u043d-\u0448\u043a\u043e\u043b\u044b \u043f\u043e\u0434\u0433\u043e\u0442\u043e\u0432\u043a\u0438 \u043a \u0415\u0413\u042d \u0438 \u041e\u0413\u042d","publisher":{"@id":"https:\/\/umschool.net\/library\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/umschool.net\/library\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"ru-RU"},{"@type":"Organization","@id":"https:\/\/umschool.net\/library\/#organization","name":"\u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a","url":"https:\/\/umschool.net\/library\/","logo":{"@type":"ImageObject","inLanguage":"ru-RU","@id":"https:\/\/umschool.net\/library\/#\/schema\/logo\/image\/","url":"\/library\/wp-content\/uploads\/2021\/06\/umlogo.svg","contentUrl":"\/library\/wp-content\/uploads\/2021\/06\/umlogo.svg","width":191,"height":48,"caption":"\u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a"},"image":{"@id":"https:\/\/umschool.net\/library\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/umschool.net\/library\/#\/schema\/person\/279fc031eb415325d4fa22462381fbd6","name":"umschool","image":{"@type":"ImageObject","inLanguage":"ru-RU","@id":"https:\/\/secure.gravatar.com\/avatar\/1e8360de1e5c6968c838aa8f62f7fae7faec4111a33db284b5f8d4ce2022cb11?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/1e8360de1e5c6968c838aa8f62f7fae7faec4111a33db284b5f8d4ce2022cb11?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/1e8360de1e5c6968c838aa8f62f7fae7faec4111a33db284b5f8d4ce2022cb11?s=96&d=mm&r=g","caption":"umschool"},"sameAs":["http:\/\/umschool.frontendie.ru"],"url":"https:\/\/umschool.net\/library\/author\/umschool\/"}]}},"_links":{"self":[{"href":"https:\/\/umschool.net\/library\/wp-json\/wp\/v2\/posts\/4344","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/umschool.net\/library\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/umschool.net\/library\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/umschool.net\/library\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/umschool.net\/library\/wp-json\/wp\/v2\/comments?post=4344"}],"version-history":[{"count":82,"href":"https:\/\/umschool.net\/library\/wp-json\/wp\/v2\/posts\/4344\/revisions"}],"predecessor-version":[{"id":23382,"href":"https:\/\/umschool.net\/library\/wp-json\/wp\/v2\/posts\/4344\/revisions\/23382"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/umschool.net\/library\/wp-json\/wp\/v2\/media\/6152"}],"wp:attachment":[{"href":"https:\/\/umschool.net\/library\/wp-json\/wp\/v2\/media?parent=4344"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/umschool.net\/library\/wp-json\/wp\/v2\/categories?post=4344"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/umschool.net\/library\/wp-json\/wp\/v2\/tags?post=4344"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}