{"id":28877,"date":"2023-09-21T14:30:28","date_gmt":"2023-09-21T14:30:28","guid":{"rendered":"https:\/\/umschool.net\/library\/?p=28877"},"modified":"2024-03-19T17:00:10","modified_gmt":"2024-03-19T17:00:10","slug":"odnorodnye-uravneniya","status":"publish","type":"post","link":"https:\/\/umschool.net\/library\/matematika\/odnorodnye-uravneniya\/","title":{"rendered":"\u041e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f"},"content":{"rendered":"\n<h3 class=\"has-text-align-center wp-block-heading\" id=\"\u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0435_\u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\"><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 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0441\u043c\u043e\u0433\u043b\u0438 \u00ab\u0437\u0430\u043c\u0435\u043d\u0438\u0442\u044c\u00bb \u041d\u043e\u0431\u0435\u043b\u0435\u0432\u0441\u043a\u0443\u044e \u043f\u0440\u0435\u043c\u0438\u044e?<\/li><li>\u0412 \u0447\u0435\u043c \u043f\u0430\u0440\u0430\u0434\u043e\u043a\u0441 \u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043d\u0430 \u043d\u043e\u043b\u044c?<\/li><li>\u0413\u0434\u0435 \u0435\u0449\u0435, \u043a\u0440\u043e\u043c\u0435 \u0448\u043a\u043e\u043b\u044b, \u043c\u043e\u0436\u043d\u043e \u0432\u0441\u0442\u0440\u0435\u0442\u0438\u0442\u044c\u0441\u044f \u0441 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u043c\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\u043c\u0438?<\/li><\/ul>\n\n\n\n<p>\u041f\u043e\u0447\u0435\u043c\u0443 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u043c \u043d\u0435 \u0434\u0430\u044e\u0442 \u041d\u043e\u0431\u0435\u043b\u0435\u0432\u0441\u043a\u0443\u044e \u043f\u0440\u0435\u043c\u0438\u044e? \u0415\u0441\u0442\u044c \u0434\u0432\u0435 \u0432\u0435\u0440\u0441\u0438\u0438: \u043f\u0435\u0440\u0432\u0430\u044f \u2013 \u041d\u043e\u0431\u0435\u043b\u044c \u043e\u0447\u0435\u043d\u044c \u043d\u0435 \u043b\u044e\u0431\u0438\u043b \u0448\u0432\u0435\u0434\u0441\u043a\u043e\u0433\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u0437-\u0437\u0430 \u043d\u0435\u0433\u043e \u043d\u0435 \u0441\u0442\u0430\u043b \u0432\u043a\u043b\u044e\u0447\u0430\u0442\u044c \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0443 \u0432 \u0441\u043f\u0438\u0441\u043e\u043a \u043d\u0430\u0443\u043a, \u0437\u0430 \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0434\u0430\u0435\u0442\u0441\u044f \u043f\u0440\u0435\u043c\u0438\u044f, \u0430 \u0432\u0442\u043e\u0440\u0430\u044f \u2013 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0442\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043d\u0430\u0443\u043a\u043e\u0439, \u0432\u0441\u043f\u043e\u043c\u043e\u0433\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0439 \u0434\u043b\u044f \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u0438\u043a\u043b\u0430\u0434\u043d\u044b\u0445 \u043e\u0431\u043b\u0430\u0441\u0442\u0435\u0439 \u0437\u043d\u0430\u043d\u0438\u0439: \u0444\u0438\u0437\u0438\u043a\u0430, \u0445\u0438\u043c\u0438\u044f, \u044d\u043a\u043e\u043d\u043e\u043c\u0438\u043a\u0430.<\/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\/09\/image-134-1024x913.png\" alt=\"\" class=\"wp-image-28879\" width=\"256\" height=\"228\" srcset=\"\/library\/wp-content\/uploads\/2023\/09\/image-134-1024x913.png 1024w, \/library\/wp-content\/uploads\/2023\/09\/image-134-300x268.png 300w, \/library\/wp-content\/uploads\/2023\/09\/image-134-768x685.png 768w, \/library\/wp-content\/uploads\/2023\/09\/image-134-1536x1370.png 1536w, \/library\/wp-content\/uploads\/2023\/09\/image-134.png 1600w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\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 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0441\u043c\u043e\u0433\u043b\u0438 \u00ab\u0437\u0430\u043c\u0435\u043d\u0438\u0442\u044c\u00bb \u041d\u043e\u0431\u0435\u043b\u0435\u0432\u0441\u043a\u0443\u044e \u043f\u0440\u0435\u043c\u0438\u044e?<\/strong><br><br>\u0425\u043e\u0442\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u043c \u043d\u0435 \u0434\u0430\u044e\u0442 \u041d\u043e\u0431\u0435\u043b\u0435\u0432\u0441\u043a\u0443\u044e \u043f\u0440\u0435\u043c\u0438\u044e, \u0443\u0447\u0435\u043d\u044b\u0435, \u0437\u0430\u043d\u0438\u043c\u0430\u044e\u0449\u0438\u0435\u0441\u044f \u0435\u0439, \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0433\u0443\u0442 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043f\u0440\u0435\u0441\u0442\u0438\u0436\u043d\u0443\u044e \u043d\u0430\u0433\u0440\u0430\u0434\u0443.<br><br>\u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0434\u043e 40 \u043b\u0435\u0442 \u043c\u043e\u0433\u0443\u0442 \u0443\u0434\u043e\u0441\u0442\u043e\u0438\u0442\u044c\u0441\u044f \u0424\u0438\u043b\u0434\u0441\u043e\u0432\u0441\u043a\u043e\u0439 \u043f\u0440\u0435\u043c\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u0432\u0440\u0443\u0447\u0430\u044e\u0442 \u0440\u0430\u0437 \u0432 \u0447\u0435\u0442\u044b\u0440\u0435 \u0433\u043e\u0434\u0430, \u0430 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u043b\u044e\u0431\u043e\u0433\u043e \u0432\u043e\u0437\u0440\u0430\u0441\u0442\u0430 \u043c\u043e\u0433\u0443\u0442 \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0410\u0431\u0435\u043b\u0435\u0432\u0441\u043a\u0443\u044e \u043f\u0440\u0435\u043c\u0438\u044e, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u0438\u0441\u0443\u0436\u0434\u0430\u0435\u0442\u0441\u044f \u0435\u0436\u0435\u0433\u043e\u0434\u043d\u043e.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u0422\u043e\u0447\u043d\u043e\u0433\u043e \u043e\u0442\u0432\u0435\u0442\u0430 \u043d\u0430 \u0432\u043e\u043f\u0440\u043e\u0441, \u043f\u043e\u0447\u0435\u043c\u0443 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u043d\u0435 \u043f\u043e\u043b\u0443\u0447\u0430\u044e\u0442 \u041d\u043e\u0431\u0435\u043b\u0435\u0432\u0441\u043a\u0443\u044e \u043f\u0440\u0435\u043c\u0438\u044e, \u043c\u044b \u0443\u0437\u043d\u0430\u0442\u044c, \u043a \u0441\u043e\u0436\u0430\u043b\u0435\u043d\u0438\u044e, \u043d\u0435 \u0441\u043c\u043e\u0436\u0435\u043c. \u041d\u043e \u0432\u0435\u0440\u0441\u0438\u044f \u043f\u0440\u043e \u0442\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u043d\u0430\u0443\u043a\u0443 \u043a\u0430\u0436\u0435\u0442\u0441\u044f \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u0430\u0432\u0434\u043e\u043f\u043e\u0434\u043e\u0431\u043d\u043e\u0439, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0441\u0435\u0433\u043e\u0434\u043d\u044f \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u0447\u0435\u043d\u044c \u043f\u043e\u043c\u043e\u0433\u0430\u044e\u0442 \u0432 \u043e\u043f\u0438\u0441\u0430\u043d\u0438\u0438 \u0444\u0438\u0437\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043f\u0440\u043e\u0446\u0435\u0441\u0441\u043e\u0432. \u042d\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442\u0441\u044f <strong>\u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u043c\u0438<\/strong>.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\"><strong>\u041e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u2013 <\/strong>\u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0432\u0441\u0435 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0435 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0438\u043c\u0435\u044e\u0442 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0438 \u043d\u0435 \u0438\u043c\u0435\u044e\u0449\u0438\u0435 \u0441\u0432\u043e\u0431\u043e\u0434\u043d\u044b\u0445 \u0447\u043b\u0435\u043d\u043e\u0432.&nbsp;<\/p>\n\n\n\n<p>\u0412 \u0442\u0430\u043a\u0438\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\u0445 \u0432 \u043b\u0435\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0438 \u0432\u0441\u0435 \u043e\u0434\u043d\u043e\u0447\u043b\u0435\u043d\u044b \u0438\u043c\u0435\u044e\u0442 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u0443\u044e \u0441\u0442\u0435\u043f\u0435\u043d\u044c, \u0441\u043f\u0440\u0430\u0432\u0430 0, \u043b\u0438\u0431\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u0438\u0432\u0435\u0441\u0442\u0438 \u043a \u0442\u0430\u043a\u043e\u043c\u0443 \u0432\u0438\u0434\u0443.&nbsp;<\/p>\n\n\n\n<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0440\u0430\u0437\u0431\u0435\u0440\u0435\u043c, \u0447\u0435\u043c \u044d\u0442\u043e\u0442 \u0442\u0438\u043f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043e\u0442\u043b\u0438\u0447\u0430\u0435\u0442\u0441\u044f \u043e\u0442 \u0434\u0440\u0443\u0433\u0438\u0445 \u0438 \u043a\u0430\u043a \u0438\u0445 \u0440\u0435\u0448\u0430\u0442\u044c.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u041e\u0434\u043d\u043e\u0440\u043e\u0434\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>\u041e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> \u2013 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0432\u0438\u0434\u0430<br>\\(a_0f^n+a_1f^{n-1}g+a_2f^{n-2}g^2+ &#8230; +a_{n-1}fg^{n-1}+a_ng^n=0\\) \u0441 \u0434\u0432\u0443\u043c\u044f \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c\u0438.&nbsp;<\/p>\n\n\n\n<p>\u042d\u0442\u043e \u043e\u0447\u0435\u043d\u044c \u043f\u043e\u0445\u043e\u0436\u0435 \u043d\u0430 \u043b\u0435\u0441\u0442\u043d\u0438\u0446\u0443, \u0432 \u0441\u043b\u0443\u0447\u0430\u0435 \u043e\u0434\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u044b \u0441\u043f\u0443\u0441\u043a\u0430\u0435\u043c\u0441\u044f \u043f\u043e \u043d\u0435\u0439, \u0438\u0434\u0435\u043c \u0441 \\(n\\)-\u043e\u0439 \u0441\u0442\u0443\u043f\u0435\u043d\u0438 \u043a \u043d\u0443\u043b\u0435\u0432\u043e\u0439: \\(n, n-1, n-2, &#8230;, 1, 0\\). \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0436\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439 \u043c\u044b \u043f\u043e \u043b\u0435\u0441\u0442\u043d\u0438\u0446\u0435 \u043f\u043e\u0434\u043d\u0438\u043c\u0430\u0435\u043c\u0441\u044f: \\(0, 1, &#8230;, n-2, n-1, n\\). \u0417\u0434\u0435\u0441\u044c \\(n\\) &#8212; \u043b\u044e\u0431\u043e\u0435 <strong>\u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, <\/strong>\u043e\u0442 \u0435\u0433\u043e \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u0442\u043e\u043b\u044c\u043a\u043e \u00ab\u0434\u043b\u0438\u043d\u0430\u00bb \u043d\u0430\u0448\u0435\u0439 \u043b\u0435\u0441\u0442\u043d\u0438\u0446\u044b.<\/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\/09\/2-3-1024x390.png\" alt=\"\" class=\"wp-image-28883\" width=\"512\" height=\"195\" srcset=\"\/library\/wp-content\/uploads\/2023\/09\/2-3-1024x390.png 1024w, \/library\/wp-content\/uploads\/2023\/09\/2-3-300x114.png 300w, \/library\/wp-content\/uploads\/2023\/09\/2-3-768x292.png 768w, \/library\/wp-content\/uploads\/2023\/09\/2-3.png 1376w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0442\u0430\u043a\u0438\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>\\(2x^2+3xy+y^2=0\\)<\/li><li>\\(2sinx+9cosx=0\\)<\/li><li>\\(4*9^x+6*4^x*3^x+18*16^x=0\\). \u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<br>\\(4*3^{2x}+6*4^x*3^x+18*4^{2x}=0\\)<\/li><\/ul>\n\n\n\n<p>\u0415\u0441\u043b\u0438 \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u0437 \u044d\u0442\u0438\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0441\u043b\u043e\u0436\u0438\u0442\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0433\u043e, \u044d\u0442\u0438 \u0441\u0443\u043c\u043c\u044b \u0431\u0443\u0434\u0443\u0442 \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u044b\u043c\u0438. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0432 \u043f\u0435\u0440\u0432\u043e\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u0441\u0443\u043c\u043c\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0433\u043e \u0440\u0430\u0432\u043d\u0430 2, \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u2013 \u0442\u0430\u043a\u0436\u0435 2 (1+1), \u0438 \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0442\u0440\u0435\u0442\u044c\u0435\u0433\u043e \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u043e\u0433\u043e \u0442\u0430\u043a\u0436\u0435 2.&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\/09\/3-2-1024x828.png\" alt=\"\" class=\"wp-image-28884\" width=\"256\" height=\"207\" srcset=\"\/library\/wp-content\/uploads\/2023\/09\/3-2-1024x828.png 1024w, \/library\/wp-content\/uploads\/2023\/09\/3-2-300x242.png 300w, \/library\/wp-content\/uploads\/2023\/09\/3-2-768x621.png 768w, \/library\/wp-content\/uploads\/2023\/09\/3-2-1536x1241.png 1536w, \/library\/wp-content\/uploads\/2023\/09\/3-2-2048x1655.png 2048w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"alignleft size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"\/library\/wp-content\/uploads\/2023\/09\/6-5-683x1024.png\" alt=\"\" class=\"wp-image-28384\" width=\"41\" height=\"62\" srcset=\"\/library\/wp-content\/uploads\/2023\/09\/6-5-683x1024.png 683w, \/library\/wp-content\/uploads\/2023\/09\/6-5-200x300.png 200w, \/library\/wp-content\/uploads\/2023\/09\/6-5-768x1152.png 768w, \/library\/wp-content\/uploads\/2023\/09\/6-5.png 1000w\" sizes=\"auto, (max-width: 41px) 100vw, 41px\" \/><\/figure><\/div>\n\n\n\n<p>\u041e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043e\u0431\u043b\u0430\u0434\u0430\u044e\u0442 \u0432\u0430\u0436\u043d\u044b\u043c \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e\u043c: \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0443\u043c\u043d\u043e\u0436\u0438\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u043c\u0438 \u043d\u0430 \u043e\u0434\u043d\u0443 \u0438 \u0442\u0443 \u0436\u0435 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0443, \u0438 \u044d\u0442\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432\u0441\u0435 \u0440\u0430\u0432\u043d\u043e \u0431\u0443\u0434\u0443\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u043c\u0438 \u0438\u0441\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f.&nbsp;<\/p>\n\n\n\n<p>\u042d\u0442\u043e \u0447\u0435\u043c-\u0442\u043e \u043f\u043e\u0445\u043e\u0436\u0435 \u043d\u0430 <a href=\"https:\/\/umschool.net\/library\/matematika\/ravenstvo-i-podobie-treugolnikov\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u043f\u043e\u0434\u043e\u0431\u043d\u044b\u0435 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0438<\/a>: \u043c\u0435\u043d\u044f\u044f \u0440\u0430\u0437\u043c\u0435\u0440 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430, \u043c\u044b \u043d\u0438\u043a\u0430\u043a \u043d\u0435 \u0438\u0437\u043c\u0435\u043d\u044f\u0435\u043c \u0435\u0433\u043e \u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u0438. \u041f\u043e \u0441\u0443\u0442\u0438, \u044d\u0442\u043e \u0442\u043e\u0442 \u0436\u0435 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \u0442\u043e\u043b\u044c\u043a\u043e \u0431\u043e\u043b\u044c\u0448\u0438\u0445 \u0438\u043b\u0438 \u043c\u0435\u043d\u044c\u0448\u0438\u0445 \u0440\u0430\u0437\u043c\u0435\u0440\u043e\u0432.&nbsp;<\/p>\n\n\n\n<p>\u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u0443\u0441\u0442\u044c \u043f\u0430\u0440\u0430 (\\(x,y\\)) \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \\(2x^2+3xy+20y^2=0\\), \u0442\u043e\u0433\u0434\u0430 \u043f\u0430\u0440\u0430 (\\(tx, ty\\)) \u0442\u0430\u043a\u0436\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435. \u041f\u0440\u043e\u0432\u0435\u0440\u0438\u043c \u044d\u0442\u043e: \\(2(tx)^2+3tx*ty+20(ty)^2=0\\), \u043c\u043e\u0436\u0435\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0442\u044c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \\(t^2\\) \u0438 \u0442\u043e\u0433\u0434\u0430 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u0438\u0441\u0445\u043e\u0434\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u0437\u043d\u0430\u0447\u0438\u0442 (\\(tx, ty\\)) \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0440\u0435\u0448\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\/09\/4-2-919x1024.png\" alt=\"\" class=\"wp-image-28885\" width=\"230\" height=\"256\" srcset=\"\/library\/wp-content\/uploads\/2023\/09\/4-2-919x1024.png 919w, \/library\/wp-content\/uploads\/2023\/09\/4-2-269x300.png 269w, \/library\/wp-content\/uploads\/2023\/09\/4-2-768x856.png 768w, \/library\/wp-content\/uploads\/2023\/09\/4-2-1379x1536.png 1379w, \/library\/wp-content\/uploads\/2023\/09\/4-2.png 1481w\" sizes=\"auto, (max-width: 230px) 100vw, 230px\" \/><\/figure><\/div>\n\n\n\n<p>\u0420\u0430\u0437\u043e\u0431\u0440\u0430\u0432\u0448\u0438\u0441\u044c \u0441 \u0442\u0435\u0440\u043c\u0438\u043d\u043e\u043b\u043e\u0433\u0438\u0435\u0439, \u0441\u0430\u043c\u043e\u0435 \u0432\u0440\u0435\u043c\u044f \u043f\u0435\u0440\u0435\u0439\u0442\u0438 \u043a \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435!<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439<\/strong><\/h2>\n\n\n\n<p>\u041b\u044e\u0431\u044b\u0435 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0440\u0435\u0448\u0430\u044e\u0442\u0441\u044f \u0434\u0435\u043b\u0435\u043d\u0438\u0435\u043c \u043e\u0431\u0435\u0438\u0445 \u0447\u0430\u0441\u0442\u0435\u0439 \u043d\u0430 \u043e\u0434\u043d\u0443 \u0438\u0437 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0431\u043e\u043b\u044c\u0448\u0435\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0441 \u0443\u0447\u0435\u0442\u043e\u043c \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u043e\u043d\u0430 \u043d\u0435 \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e. \u0414\u0430\u043b\u0435\u0435 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0441\u043e\u0432\u0435\u0440\u0448\u0438\u0442\u044c \u0437\u0430\u043c\u0435\u043d\u0443 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u0438 \u0440\u0435\u0448\u0438\u0442\u044c \u043f\u043e\u043b\u0443\u0447\u0438\u0432\u0448\u0435\u0435\u0441\u044f \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0435 \u0438\u043b\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435.<\/p>\n\n\n\n<p>\u041f\u043e\u0434\u0440\u043e\u0431\u043d\u0435\u0435 \u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u0438 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u043e\u0447\u0438\u0442\u0430\u0442\u044c \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 <a href=\"https:\/\/umschool.net\/library\/matematika\/linejnye-kvadratnye-i-kubicheskie-uravneniya-2\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u00ab\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\u00bb<\/a>.<\/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 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong>:<br><br><strong>1 \u0448\u0430\u0433<\/strong>: \u0420\u0430\u0437\u0434\u0435\u043b\u0438\u0442\u044c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u043e\u0434\u043d\u0443 \u0438\u0437 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0432 \u0431\u043e\u043b\u044c\u0448\u0435\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u0441 \u0443\u0447\u0435\u0442\u043e\u043c \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u044d\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e.<br>\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \\(a_0f^n+a_1f^{n-1}g+a_2f^{n-2}g^2+ &#8230; +a_{n-1}fg^{n-1}+a_ng^n=0\\) \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0442\u044c \u0438\u043b\u0438 \u043d\u0430 \\(f^n\\), \u0438\u043b\u0438 \u043d\u0430 \\(g^n\\).<br><br><strong>2 \u0448\u0430\u0433<\/strong>: \u0421\u0434\u0435\u043b\u0430\u0442\u044c <strong>\u0437\u0430\u043c\u0435\u043d\u0443 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445.<\/strong><br><br><strong>3 \u0448\u0430\u0433: <\/strong>\u0420\u0435\u0448\u0438\u0442\u044c \u043f\u043e\u043b\u0443\u0447\u0438\u0432\u0448\u0435\u0435\u0441\u044f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435.<br><br><strong>4 \u0448\u0430\u0433<\/strong>: \u0421\u0434\u0435\u043b\u0430\u0442\u044c \u043e\u0431\u0440\u0430\u0442\u043d\u0443\u044e \u0437\u0430\u043c\u0435\u043d\u0443.<\/p>\n\n\n\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u0440\u0435\u0448\u0430\u0442\u044c \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0442\u0438\u043f\u044b \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439: \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0438 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f.&nbsp;<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u041e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\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>\u041e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0431\u044b\u0432\u0430\u044e\u0442 \u0434\u0432\u0443\u0445 \u0442\u0438\u043f\u043e\u0432:<\/strong><br>1. \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0435\u0440\u0432\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u2013 \\(acos{x}+bsin{x}=0\\)<br>2. \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0432\u0442\u043e\u0440\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u2013 \\(acos^2x+bcos{x}sin{x}+csin^2x=0\\)<\/p>\n\n\n\n<p>\u0420\u0430\u0437\u0431\u0435\u0440\u0435\u043c \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f: \\(3sinx+2cosx=0\\).<\/p>\n\n\n\n<p>\u041d\u0430\u0438\u0431\u043e\u043b\u044c\u0448\u0430\u044f \u0441\u0442\u0435\u043f\u0435\u043d\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u2013 \u0435\u0434\u0438\u043d\u0438\u0446\u0430, \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u043c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \\(cosx \u2260 0\\). \u042d\u0442\u043e \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0432\u0435\u0440\u043d\u043e, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u0435\u0441\u043b\u0438 \\(cosx = 0\\), \u0442\u043e \\(sinx = 1\\) \u0438\u043b\u0438 \\(-1\\), \u0442\u043e\u0433\u0434\u0430 \\(-3=0\\) \u0438\u043b\u0438 \\(3=0\\), \u0447\u0442\u043e \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u0412 \u0447\u0435\u043c \u043f\u0430\u0440\u0430\u0434\u043e\u043a\u0441 \u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043d\u0430 \u043d\u043e\u043b\u044c?<\/strong><br><br>\u0414\u0435\u043b\u0435\u043d\u0438\u0435 \u043d\u0430 \u043d\u043e\u043b\u044c \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e, \u0442\u0430\u043a \u043a\u0430\u043a \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u043b\u044e\u0431\u043e\u0433\u043e \u0447\u0438\u0441\u043b\u0430 \u043d\u0430 \u043d\u043e\u043b\u044c \u0434\u0430\u0435\u0442 \u0432 \u0438\u0442\u043e\u0433\u0435 \u043d\u043e\u043b\u044c. \u0422\u043e\u0433\u0434\u0430, \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0432 \u043b\u044e\u0431\u043e\u0435 \u0447\u0438\u0441\u043b\u043e, \u043e\u0442\u043b\u0438\u0447\u043d\u043e\u0435 \u043e\u0442 \u043d\u0443\u043b\u044f, \u043d\u0430 \u043d\u043e\u043b\u044c, \u043c\u044b, \u043f\u043e\u043b\u0443\u0447\u0430\u044f \u043b\u044e\u0431\u0443\u044e \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0443, \u043d\u0430\u0440\u0443\u0448\u0438\u043c \u044d\u0442\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u043e.<br><br>\u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u043f\u043e\u043f\u0440\u043e\u0431\u0443\u0435\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0442\u044c \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u043d\u0430 \u043d\u043e\u043b\u044c: \\(\\frac{7}{0}=x\\). \u0422\u043e\u0433\u0434\u0430 \\(0*x=7\\), \u043d\u043e \u044d\u0442\u043e \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e, \u043a\u0430\u043a\u043e\u0435 \u0431\u044b \u0447\u0438\u0441\u043b\u043e \u0432\u043c\u0435\u0441\u0442\u043e x \u043c\u044b \u043d\u0438 \u0432\u0437\u044f\u043b\u0438.&nbsp;<\/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\/09\/5-2-1024x964.png\" alt=\"\" class=\"wp-image-28887\" width=\"256\" height=\"241\" srcset=\"\/library\/wp-content\/uploads\/2023\/09\/5-2-1024x964.png 1024w, \/library\/wp-content\/uploads\/2023\/09\/5-2-300x282.png 300w, \/library\/wp-content\/uploads\/2023\/09\/5-2-768x723.png 768w, \/library\/wp-content\/uploads\/2023\/09\/5-2-1536x1446.png 1536w, \/library\/wp-content\/uploads\/2023\/09\/5-2-2048x1928.png 2048w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center\">\\(3\\frac{sinx}{cosx}+2\\frac{cosx}{cosx}=0\\)<\/p>\n\n\n\n<p>\u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \\(\\frac{sin x}{cos x}=tg x\\):&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(3tgx+2=0\\)<br>\u041f\u0443\u0441\u0442\u044c \\(t =tgx\\)<br>\\(3t+2=0\\)<br>\\(3t=-2\\)<br>\\(t=-\\frac{2}{3}\\)<\/p>\n\n\n\n<p>\u041f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043c \u043e\u0431\u0440\u0430\u0442\u043d\u0443\u044e \u0437\u0430\u043c\u0435\u043d\u0443:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(tgx=-\\frac{2}{3}\\)<\/p>\n\n\n\n<p>\u0420\u0435\u0448\u0438\u043c <a href=\"https:\/\/umschool.net\/library\/matematika\/formuly-trigonometrii-i-prostejshie-uravneniya\/#part7\" target=\"_blank\" rel=\"noreferrer noopener\">\u043f\u0440\u043e\u0441\u0442\u0435\u0439\u0448\u0435\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/a>:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(x = arctg(-\\frac{2}{3})+\u03c0n, n \u220a Z\\)<br>\\(x =-arctg(\\frac{2}{3})+\u03c0n, n \u220a Z\\)<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\">\u0422\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u044e\u0442\u0441\u044f \u0432 <strong>\u0437\u0430\u0434\u0430\u043d\u0438\u0438 \u211612 \u0415\u0413\u042d (\u211613 \u0432 \u0415\u0413\u042d 2024 \u0433\u043e\u0434\u0430) \u043f\u043e \u043f\u0440\u043e\u0444\u0438\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435<\/strong>.<br><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435.<\/strong> <em>\u0430) \u0420\u0435\u0448\u0438\u0442\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 <\/em>\\(2sin2x+4cos^2x=-2cos2x\\)<br><em>\u0431) \u0423\u043a\u0430\u0436\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>\\([\u03c0; \\frac{3\u03c0}{2}]\\)<br><br><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435. <\/strong>a) \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 \u0441\u0442\u043e\u0440\u043e\u043d\u0443:&nbsp;<br><br>\\(2sin2x + 4cos^2x+2cos2x=0\\)<br><br><a href=\"https:\/\/umschool.net\/library\/matematika\/formuly-trigonometrii-i-prostejshie-uravneniya\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0420\u0430\u0441\u043a\u0440\u043e\u0435\u043c \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b<\/a>:<br><br>\\(sin2x = 2sinxcosx\\)<br>\\(cos2x=cos^2x-sin^2x\\)<br><br>\u0422\u043e\u0433\u0434\u0430 \\(4sinxcosx+4cos^2x+2(cos^2x-sin^2x)=0\\)<br>\\(4sinxcosx+4cos^2x+2cos^2x-2sin^2x=0\\)<br>\\(4sinxcosx+6cos^2x-2sin^2x=0\\)<br>\\(6cos^2x+4sinxcosx-2sin^2x=0 | :2\\)<br><br>\u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043c\u044b \u0440\u0435\u0448\u0430\u0435\u043c \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u043d\u0430\u043c \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0435\u0433\u043e \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0442\u044c \u043d\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u0432 \u0431\u043e\u043b\u044c\u0448\u0435\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438, \u0442\u043e \u0435\u0441\u0442\u044c \u043d\u0430 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0438\u043b\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442 \u0441\u0438\u043d\u0443\u0441\u0430. \u0420\u0430\u0437\u0434\u0435\u043b\u0438\u043c \u043d\u0430 \u043a\u043e\u0441\u0438\u043d\u0443\u0441:&nbsp;<br><br>\\(3cos^2x + 2sinxcosx-sin^2x=0 | : cos^2x \u2260 0\\)<br><br>\\(cos^2x \u2260 0\\), \u0442\u0430\u043a \u043a\u0430\u043a \u0435\u0441\u043b\u0438 \\(cosx=0\\), \u0442\u043e \\(sinx=1\\) \u0438\u043b\u0438 \\(-1\\), \u0442\u043e\u0433\u0434\u0430 \\(-1=0\\), \u0447\u0442\u043e \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e.<br><br>\\(3+2\\frac{sinx}{cosx}-(\\frac{sinx}{cosx})^2=0\\)<br><br>\u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \\(\\frac{sinx}{cosx}=tgx\\), \u0442\u043e:<br><br>\\(-tg^2x+2tgx+3=0\\)<br>\u041f\u0443\u0441\u0442\u044c \\(t = tgx\\)<br>\\(-t^2+2t+3=0\\)<br><br>\u0420\u0435\u0448\u0438\u043c <a href=\"https:\/\/umschool.net\/library\/matematika\/linejnye-kvadratnye-i-kubicheskie-uravneniya-2\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/a>:<br><br>\\(D =b^2-4ac = 2^2-4*3*(-1)=4+12=16\\)<br>\\(t_1=\\frac{-b-\\sqrt{D}}2a=\\frac{-2-4}{-2}=3\\)<br>\\(t_2=\\frac{-b+\\sqrt{D}}2a=\\frac{-2+4}{-2}=-1\\)<br><br>\u041e\u0431\u0440\u0430\u0442\u043d\u0430\u044f \u0437\u0430\u043c\u0435\u043d\u0430:<br><br>\\(tgx = 3\\) \u0438\u043b\u0438 \\(tgx=-1\\)<br>\\(x = arctg(3)+\u03c0n, n \u220a Z\\) \u0438\u043b\u0438 \\(x = arctg(-1)+\u03c0n =-\\frac{\u03c0}{4}+\u03c0n, n \u220a Z\\)<br><br>\u0431) \u041e\u0442\u0431\u0435\u0440\u0435\u043c \u043a\u043e\u0440\u043d\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e <a href=\"https:\/\/umschool.net\/library\/matematika\/trigonometricheskaya-okruzhnost-chast-1\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u043e\u043a\u0440\u0443\u0436\u043d\u043e\u0441\u0442\u0438<\/a><\/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\/09\/6-7.png\" alt=\"\" class=\"wp-image-28890\" width=\"401\" height=\"346\" srcset=\"\/library\/wp-content\/uploads\/2023\/09\/6-7.png 801w, \/library\/wp-content\/uploads\/2023\/09\/6-7-300x259.png 300w, \/library\/wp-content\/uploads\/2023\/09\/6-7-768x663.png 768w\" sizes=\"auto, (max-width: 401px) 100vw, 401px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\"><strong>\u041e\u0442\u0432\u0435\u0442: <\/strong>\u0430) \\(arctg(3)+\u03c0n, -\\frac{\u03c0}{4}+\u03c0n, n \u220a Z\\)<br>\u0431) \\(arctg(3)+\u03c0\\)<\/p>\n\n\n\n<p>\u041e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0433\u0443\u0442 \u0431\u044b\u0442\u044c \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u043c\u0438.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>\u041e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong><\/h3>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\"><strong>\u041e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0431\u044b\u0432\u0430\u044e\u0442 \u0434\u0432\u0443\u0445 \u0442\u0438\u043f\u043e\u0432:<\/strong><br>1. \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0435\u0440\u0432\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u2013 \\(af^x+bg^x=0\\)<br>2. \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0432\u0442\u043e\u0440\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u2013 \\(af^{2x}+bf^xg^x+cg^{2x}=0\\)<\/p>\n\n\n\n<p>\u0412 \u0441\u043b\u0443\u0447\u0430\u0435 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0445 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043c\u044b \u0434\u0435\u0439\u0441\u0442\u0432\u0443\u0435\u043c \u0442\u0430\u043a \u0436\u0435, \u043a\u0430\u043a \u0438 \u0432 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\u0445, \u0442\u043e \u0435\u0441\u0442\u044c \u0434\u0435\u043b\u0438\u043c \u043d\u0430 \u0447\u043b\u0435\u043d \u0441\u043e \u0441\u0442\u0430\u0440\u0448\u0435\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u044c\u044e.<\/p>\n\n\n\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u0434\u0435\u0439\u0441\u0442\u0432\u043e\u0432\u0430\u0442\u044c \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0433\u043e \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043f\u0435\u0440\u0432\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(4^x=\\frac{3}{4}*3^x\\)<\/p>\n\n\n\n<p>\u0420\u0430\u0437\u0434\u0435\u043b\u0438\u043c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \\(3^x \u2260 0\\), \u0442\u0430\u043a \u043a\u0430\u043a \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u0432 \u043b\u044e\u0431\u043e\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0431\u043e\u043b\u044c\u0448\u0435 \u043d\u0443\u043b\u044f.&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\((\\frac{4}{3})^x=\\frac{3}{4}\\)<br>\\((\\frac{4}{3})^x=(\\frac{4}{3})^{-1}\\)<br>\\(x=-1\\)<\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\">\u0420\u0430\u0437\u0431\u0435\u0440\u0435\u043c \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043c\u043e\u0436\u0435\u0442 \u0432\u0441\u0442\u0440\u0435\u0442\u0438\u0442\u044c\u0441\u044f \u0432 <strong>\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 \u0432 \u0437\u0430\u0434\u0430\u043d\u0438\u0438 \u211613.<\/strong><br><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435. <\/strong><em>\u0430) \u0420\u0435\u0448\u0438\u0442\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 <\/em>\\(9^x-7*6^x+12*4^x=0\\)<br><em>\u0431) \u0423\u043a\u0430\u0436\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\u0435\u0433\u043e \u043e\u0442\u0440\u0435\u0437\u043a\u0443 <\/em>\\([1; 3]\\).<br><br><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435. <\/strong>\u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0438\u0441\u0445\u043e\u0434\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435: \\(3^{2x}-7*3^x*2^x+12*2^{2x}=0\\)<br><br>\u0420\u0430\u0437\u0434\u0435\u043b\u0438\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043d\u0430 \\(2^{2x} \u2260 0\\), \u0442\u0430\u043a \u043a\u0430\u043a \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \u0432\u0441\u0435\u0433\u0434\u0430 \u0431\u043e\u043b\u044c\u0448\u0435 \u043d\u0443\u043b\u044f.<br><br>\\((\\frac{3}{2})^{2x}-7*(\\frac{3}{2})^x+12=0\\)<br>\u041f\u0443\u0441\u0442\u044c \\(t = (\\frac{3}{2})^x\\)<br>\\(t^2-7t+12=0\\)<br>\\(D =b^2-4ac = (-7)^2-4*12=49+48=1\\)<br>\\(t_1=\\frac{-b-\\sqrt{D}}{2a}=\\frac{7-1}{2}=3\\)<br>\\(t_2=\\frac{-b+\\sqrt{D}}{2a}=\\frac{7+1}{2}=4\\)<br><br>\u041e\u0431\u0440\u0430\u0442\u043d\u0430\u044f \u0437\u0430\u043c\u0435\u043d\u0430:<br><br>\\((\\frac{3}{2})^x=3\\) \u0438\u043b\u0438 \\((\\frac{3}{2})^x=4\\)<br>\\(x = log_{\\frac{3}{2}}3\\) \u0438\u043b\u0438 \\(x= log_{\\frac{3}{2}}4\\)<br><br>\u0431) \u041e\u0442\u0431\u043e\u0440 \u043a\u043e\u0440\u043d\u0435\u0439 \u043d\u0430 \u043e\u0442\u0440\u0435\u0437\u043a\u0435:<br><br>\\((\\frac{3}{2})^x=3\\)<br>\\((\\frac{3}{2})^1&lt;3&lt;(\\frac{3}{2})^3\\)<br>\\((\\frac{3}{2})^1&lt;(\\frac{3}{2})^x&lt;(\\frac{3}{2})^3\\)<br>\\(1&lt;x&lt;3\\)<br><br>\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \\(x = log_{\\frac{3}{2}}3 \u220a [1; 3]\\).<br><br>\\((\\frac{3}{2})^x=4\\)<br>\\((\\frac{3}{2})^3&lt;4\\)<br>\\((\\frac{3}{2})^3&lt;(\\frac{3}{2})^x\\)<br>\\(x&gt;3\\)<br><br>\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \\(x = log_{\\frac{3}{2}}4 \u2209 [1; 3]\\).<br><br><strong>\u041e\u0442\u0432\u0435\u0442<\/strong>: a) \\(log_{\\frac{3}{2}}3, log_{\\frac{3}{2}}4\\)<br>b) \\(log_{\\frac{3}{2}}3\\)<\/p>\n\n\n\n<p>\u041e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u2013 \u0432\u0430\u0436\u043d\u0435\u0439\u0448\u0438\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0439 \u0438\u043d\u0441\u0442\u0440\u0443\u043c\u0435\u043d\u0442, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0432 \u0440\u0430\u0437\u043b\u0438\u0447\u043d\u044b\u0445 \u0441\u0444\u0435\u0440\u0430\u0445, \u0431\u0435\u0437 \u043d\u0438\u0445 \u0441\u043b\u043e\u0436\u043d\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0441\u043e\u0432\u0440\u0435\u043c\u0435\u043d\u043d\u0443\u044e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0443 \u0432 \u0442\u043e\u043c \u0432\u0438\u0434\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u043c\u044b \u0435\u0435 \u0437\u043d\u0430\u0435\u043c \u0441\u0435\u0439\u0447\u0430\u0441.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u0413\u0434\u0435 \u0435\u0449\u0435, \u043a\u0440\u043e\u043c\u0435 \u0448\u043a\u043e\u043b\u044b, \u043c\u043e\u0436\u043d\u043e \u0432\u0441\u0442\u0440\u0435\u0442\u0438\u0442\u044c\u0441\u044f \u0441 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u043c\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\u043c\u0438?<\/strong><br><br>\u041f\u0440\u0438 \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u0438 \u0432\u044b\u0441\u0448\u0435\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0432 \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0435 \u043f\u043e\u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u043e\u0432\u044b\u0439 \u0442\u0438\u043f \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u2013 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u0442\u043e \u0435\u0441\u0442\u044c \u0442\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0443\u0447\u0430\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0435 \u0442\u043e\u043b\u044c\u043a\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043d\u043e \u0438 \u0435\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f.<br><br>\u041e\u0434\u0438\u043d \u0438\u0437 \u0432\u0438\u0434\u043e\u0432 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u2013 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0435 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0442\u0430\u043a\u0436\u0435 \u043e\u0431\u043b\u0430\u0434\u0430\u044e\u0442 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e\u043c \u00ab\u043e\u0431\u044b\u0447\u043d\u044b\u0445\u00bb \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439: \u0435\u0441\u043b\u0438 (x, y) \u2013 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0438\u0441\u0445\u043e\u0434\u043d\u043e\u0433\u043e \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0433\u043e \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u0442\u043e (tx, ty) \u0442\u0430\u043a\u0436\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435.<\/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\/09\/7-2-1024x872.png\" alt=\"\" class=\"wp-image-28896\" width=\"256\" height=\"218\" srcset=\"\/library\/wp-content\/uploads\/2023\/09\/7-2-1024x872.png 1024w, \/library\/wp-content\/uploads\/2023\/09\/7-2-300x256.png 300w, \/library\/wp-content\/uploads\/2023\/09\/7-2-768x654.png 768w, \/library\/wp-content\/uploads\/2023\/09\/7-2-1536x1308.png 1536w, \/library\/wp-content\/uploads\/2023\/09\/7-2.png 1969w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p>\u0427\u0442\u043e\u0431\u044b \u0443\u0436\u0435 \u0441\u0435\u0439\u0447\u0430\u0441 \u043d\u0430\u0447\u0430\u0442\u044c \u0433\u043e\u0442\u043e\u0432\u0438\u0442\u044c\u0441\u044f \u043a \u0443\u0447\u0435\u0431\u0435 \u0432&nbsp; \u0443\u043d\u0438\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0435, \u0447\u0438\u0442\u0430\u0439\u0442\u0435 \u043d\u0430\u0448\u0443 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0441\u0442\u0430\u0442\u044c\u044e \u00ab<a href=\"https:\/\/umschool.net\/library\/matematika\/proizvodnaya\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u041f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f<\/a>\u00bb.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\"><strong>\u0422\u0435\u0440\u043c\u0438\u043d\u044b<\/strong><\/h2>\n\n\n\n<p><strong>\u041a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0430 <\/strong>\u2013 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0430, \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043d\u0435 \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f.&nbsp;<\/p>\n\n\n\n<p><strong>\u0417\u0430\u043c\u0435\u043d\u0430 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u2013 <\/strong>\u044d\u0442\u043e \u0442\u0430\u043a\u043e\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u0440\u0435\u0448\u0435\u043d\u0438\u044f, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0432 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 (\u0438\u043b\u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e) \u0432\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u043d\u043e\u0432\u0430\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u0430\u044f, \u0432 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0435 \u0447\u0435\u0433\u043e \u043e\u043d\u043e \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u043e\u0441\u0442\u044b\u043c.<\/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>\u041e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0435<\/strong> <strong>\u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435<\/strong> \u2013 \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441 \u0434\u0432\u0443\u043c\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438 \u0431\u0435\u0437 \u0441\u0432\u043e\u0431\u043e\u0434\u043d\u043e\u0433\u043e \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u0430, \u0430 \u0432 \u043a\u0430\u0436\u0434\u043e\u043c \u0438\u0437 \u0441\u043b\u0430\u0433\u0430\u0435\u043c\u044b\u0445 \u043d\u0430\u0431\u043b\u044e\u0434\u0430\u0435\u0442\u0441\u044f \u043e\u0434\u0438\u043d\u0430\u043a\u043e\u0432\u0430\u044f \u0441\u0443\u043c\u043c\u0430 \u0441\u0442\u0435\u043f\u0435\u043d\u0435\u0439.<\/li><li>\u0421\u0432\u043e\u0439\u0441\u0442\u0432\u043e \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f: \u0435\u0441\u043b\u0438 \u043f\u0430\u0440\u0430 (x, y) \u2013 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u043f\u0430\u0440\u0430 (tx, ty) \u0442\u0430\u043a\u0436\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435.<\/li><li>\u041f\u0440\u0438 \u0440\u0435\u0448\u0435\u043d\u0438\u0438 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u0442\u044c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u044d\u0442\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u043e\u0434\u043d\u0443 \u0438\u0437 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0432 \u0431\u043e\u043b\u044c\u0448\u0435\u0439 \u0441\u0442\u0435\u043f\u0435\u043d\u0438 \u0441 \u0443\u0447\u0435\u0442\u043e\u043c \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u044d\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043d\u0435 \u0440\u0430\u0432\u043d\u0430 \u043d\u0443\u043b\u044e.<\/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>\u041a\u0430\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u043c?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(3x+y^2=0\\)<\/li><li>\\(3sin^3x-cos^2x=0\\)<\/li><li>\\(5^x+5^x*7^x=0\\)<\/li><li>\\(5x^3-4x^2y+6xy^2+3y^3=0\\)<\/li><\/ol>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 2.<\/strong><br>\u0415\u0441\u043b\u0438 \u043f\u0430\u0440\u0430 \u0447\u0438\u0441\u0435\u043b (3,2) \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u043a\u0430\u043a\u0430\u044f \u043f\u0430\u0440\u0430 \u0447\u0438\u0441\u0435\u043b \u0442\u0430\u043a\u0436\u0435 \u0431\u0443\u0434\u0435\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>(6, 6)<\/li><li>(5, 4)<\/li><li>(9, 6)<\/li><li>(4, 3)<\/li><\/ol>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 3.<\/strong><br>\u0427\u0442\u043e \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0433\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \\(2x^2-xy-y^2=0\\)?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(x=2, y=2\\)<\/li><li>\\(x=1, y=3\\)<\/li><li>\\(x=2, y=-2\\)<\/li><li>\\(x=-2, y=2\\)<\/li><\/ol>\n\n\n\n<p><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 4.<\/strong><br>\u0427\u0442\u043e \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \\(5^x=6^x\\)?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(0,5\\)<\/li><li>\\(0\\)<\/li><li>\\(1\\)<\/li><li>\\(2\\)<\/li><\/ol>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 5.<\/strong><br>\u0427\u0442\u043e \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \\(cos^2x+2*cosx*sinx-5sin^2x=0\\)?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(x = arcctg(-1-\\sqrt{6})+\u03c0n;arcctg(1+\\sqrt{6})+\u03c0n, n \u220a Z\\)<\/li><li>\\(x = arcctg(-1-\\sqrt{6})+\u03c0n, n \u220a Z\\)<\/li><li>\\(arcctg(1+\\sqrt{6})+\u03c0n, n \u220a Z\\)<\/li><li>\\(x = arcctg(-1-\\sqrt{6})+\u03c0n;arcctg(-1+\\sqrt{6})+\u03c0n, n \u220a Z\\)<\/li><\/ol>\n\n\n\n<p><strong>\u041e\u0442\u0432\u0435\u0442\u044b: 1. \u2014 <\/strong>4;<strong> 2. \u2014 <\/strong>3;<strong> 3. \u2014 <\/strong>1;<strong> 4. \u2014 <\/strong>2; <strong>5.<\/strong><strong>\u2014 <\/strong>4.<\/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 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0441\u043c\u043e\u0433\u043b\u0438 \u00ab\u0437\u0430\u043c\u0435\u043d\u0438\u0442\u044c\u00bb \u041d\u043e\u0431\u0435\u043b\u0435\u0432\u0441\u043a\u0443\u044e \u043f\u0440\u0435\u043c\u0438\u044e? \u0412 \u0447\u0435\u043c \u043f\u0430\u0440\u0430\u0434\u043e\u043a\u0441 \u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043d\u0430 \u043d\u043e\u043b\u044c? \u0413\u0434\u0435 \u0435\u0449\u0435, \u043a\u0440\u043e\u043c\u0435 \u0448\u043a\u043e\u043b\u044b, \u043c\u043e\u0436\u043d\u043e \u0432\u0441\u0442\u0440\u0435\u0442\u0438\u0442\u044c\u0441\u044f \u0441 \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u044b\u043c\u0438 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f\u043c\u0438? \u041f\u043e\u0447\u0435\u043c\u0443 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430\u043c \u043d\u0435 \u0434\u0430\u044e\u0442 \u041d\u043e\u0431\u0435\u043b\u0435\u0432\u0441\u043a\u0443\u044e \u043f\u0440\u0435\u043c\u0438\u044e? \u0415\u0441\u0442\u044c \u0434\u0432\u0435 \u0432\u0435\u0440\u0441\u0438\u0438: \u043f\u0435\u0440\u0432\u0430\u044f \u2013 \u041d\u043e\u0431\u0435\u043b\u044c \u043e\u0447\u0435\u043d\u044c \u043d\u0435 \u043b\u044e\u0431\u0438\u043b \u0448\u0432\u0435\u0434\u0441\u043a\u043e\u0433\u043e \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u0438\u0437-\u0437\u0430 \u043d\u0435\u0433\u043e \u043d\u0435 \u0441\u0442\u0430\u043b \u0432\u043a\u043b\u044e\u0447\u0430\u0442\u044c \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0443 \u0432 \u0441\u043f\u0438\u0441\u043e\u043a \u043d\u0430\u0443\u043a, \u0437\u0430 \u043a\u043e\u0442\u043e\u0440\u044b\u0435 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":36238,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[27,1197],"class_list":["post-28877","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-matematika","tag-odnorodnye-uravneniya"],"yoast_head":"<!-- This site is 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