{"id":33965,"date":"2024-02-23T10:07:07","date_gmt":"2024-02-23T10:07:07","guid":{"rendered":"https:\/\/umschool.net\/library\/?p=33965"},"modified":"2024-02-23T10:11:08","modified_gmt":"2024-02-23T10:11:08","slug":"neravenstva-s-parametrami","status":"publish","type":"post","link":"https:\/\/umschool.net\/library\/matematika\/neravenstva-s-parametrami\/","title":{"rendered":"\u041d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438"},"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>\u0414\u043e\u043b\u0436\u0435\u043d \u043b\u0438 \u043e\u0442\u0432\u0435\u0442 \u0431\u044b\u0442\u044c \u043a\u0440\u0430\u0441\u0438\u0432\u044b\u043c \u0447\u0438\u0441\u043b\u043e\u043c?<\/li><li>\u041a\u043e\u0433\u0434\u0430 \u043f\u043e\u044f\u0432\u0438\u043b\u0438\u0441\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438?<\/li><li>\u041f\u0430\u0440\u0430\u0431\u043e\u043b\u0430: \u043a\u0430\u043a \u043e\u043d\u0430 \u043f\u043e\u043c\u043e\u0436\u0435\u0442 \u0432\u0430\u043c \u043d\u0430 \u0415\u0413\u042d?<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u0435\u0434\u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0435 \u0437\u0430\u0434\u0430\u043d\u0438\u0435 \u0432 \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. \u0412\u043e\u0437\u043c\u043e\u0436\u043d\u043e, \u0441\u0430\u043c\u043e\u0435 \u0441\u043b\u043e\u0436\u043d\u043e\u0435. \u041d\u043e \u0442\u0430\u043a \u043b\u0438 \u043e\u043d\u043e \u043f\u0443\u0433\u0430\u044e\u0449\u0435, \u043a\u0430\u043a \u043e \u043d\u0435\u043c \u0433\u043e\u0432\u043e\u0440\u044f\u0442? \u0423\u0437\u043d\u0430\u0435\u043c \u043e\u0431 \u044d\u0442\u043e\u043c \u0432 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435!<\/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\/2024\/02\/1-25-1024x947.png\" alt=\"\" class=\"wp-image-33969\" width=\"512\" height=\"474\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/1-25-1024x947.png 1024w, \/library\/wp-content\/uploads\/2024\/02\/1-25-300x277.png 300w, \/library\/wp-content\/uploads\/2024\/02\/1-25-768x710.png 768w, \/library\/wp-content\/uploads\/2024\/02\/1-25-1536x1420.png 1536w, \/library\/wp-content\/uploads\/2024\/02\/1-25.png 1868w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u041b\u0438\u043d\u0435\u0439\u043d\u044b\u0435-\u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430-\u0438-\u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430,-\u043f\u0440\u0438\u0432\u043e\u0434\u0438\u043c\u044b\u0435-\u043a-\u043b\u0438\u043d\u0435\u0439\u043d\u044b\u043c-\u0441-\u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c\"><strong>\u041b\u0438\u043d\u0435\u0439\u043d\u044b\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430, \u043f\u0440\u0438\u0432\u043e\u0434\u0438\u043c\u044b\u0435 \u043a \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u043c \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0418\u0442\u0430\u043a, \u0431\u0443\u0434\u0435\u043c \u0438\u0437\u0443\u0447\u0430\u0442\u044c \u044d\u0442\u0443 \u0442\u0435\u043c\u0443 \u0441\u0440\u0430\u0437\u0443 \u0436\u0435 \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u0445, \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u0442\u0435\u043e\u0440\u0438\u0438 \u0442\u0443\u0442 \u043d\u0435 \u0442\u0430\u043a \u043c\u043d\u043e\u0433\u043e. \u0423\u0441\u043f\u0435\u0448\u043d\u043e\u0435 \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u0430 \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043d\u043d\u044b\u0445 \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432: \u0447\u0435\u043c \u0431\u043e\u043b\u044c\u0448\u0435, \u0442\u0435\u043c \u043b\u0443\u0447\u0448\u0435! \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0432 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u0445 \u043d\u0435\u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0434\u0435\u043b\u0438\u0442\u044c \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0431\u0443\u0434\u0435\u0442 \u043f\u043e\u0434\u0445\u043e\u0434\u0438\u0442\u044c \u043a\u043e \u0432\u0441\u0435\u043c \u0443\u0441\u043b\u043e\u0432\u0438\u044f\u043c, \u0442\u043e \u0442\u0443\u0442 \u0432\u0441\u0435 \u0437\u0430\u0432\u0438\u0441\u0438\u0442 \u043e\u0442 \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0440\u0430\u0441\u0441\u0443\u0436\u0434\u0435\u043d\u0438\u0439. \u0418\u043c\u0435\u043d\u043d\u043e \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0447\u0435\u043c \u0431\u043e\u043b\u044c\u0448\u0435 \u0440\u0435\u0448\u0435\u043d\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u043e\u0432, \u0442\u0435\u043c \u043b\u0443\u0447\u0448\u0435, \u0445\u043e\u0442\u044f \u0431\u044b \u043f\u043e\u0442\u043e\u043c\u0443, \u0447\u0442\u043e \u0440\u0435\u0448\u0430\u0442\u044c \u0437\u043d\u0430\u043a\u043e\u043c\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430\u043c\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0449\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\/2024\/02\/2-22-957x1024.png\" alt=\"\" class=\"wp-image-33970\" width=\"239\" height=\"256\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/2-22-957x1024.png 957w, \/library\/wp-content\/uploads\/2024\/02\/2-22-280x300.png 280w, \/library\/wp-content\/uploads\/2024\/02\/2-22-768x822.png 768w, \/library\/wp-content\/uploads\/2024\/02\/2-22-1435x1536.png 1435w, \/library\/wp-content\/uploads\/2024\/02\/2-22.png 1525w\" sizes=\"auto, (max-width: 239px) 100vw, 239px\" \/><\/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\/2024\/02\/photo1691152501-2-417x1024.jpeg\" alt=\"\" class=\"wp-image-33811\" width=\"20\" height=\"49\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/photo1691152501-2-417x1024.jpeg 417w, \/library\/wp-content\/uploads\/2024\/02\/photo1691152501-2-122x300.jpeg 122w, \/library\/wp-content\/uploads\/2024\/02\/photo1691152501-2.jpeg 521w\" sizes=\"auto, (max-width: 20px) 100vw, 20px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0430\u043f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e<strong> \u0440\u0435\u0448\u0438\u0442\u044c \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c<\/strong> \u2014 \u043d\u0430\u0439\u0442\u0438 \u0432\u0441\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <em>x<\/em> \u043f\u0440\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 <em>a<\/em>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0420\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u043c \u0432\u0441\u0435 \u0441\u043b\u0443\u0447\u0430\u0438 \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 \u043f\u0440\u0438 <em>x<\/em>.<\/strong><\/p>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\u0420\u0435\u0448\u0438\u043c \u0437\u0430\u0434\u0430\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043c\u043e\u0436\u0435\u0442 \u043f\u043e\u043f\u0430\u0441\u0442\u044c\u0441\u044f \u043d\u0430 <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 \u211618.\u00a0<\/strong><br><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435. <\/strong><em>\u0420\u0435\u0448\u0438\u0442\u044c \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e <\/em>\\(\\frac{x(a-2)}{a-1}-\\frac{3a}{4}\\leq 2x-a\\)<em> \u043f\u0440\u0438 <\/em>\\(\u0430 \u2260 1\\)<em>.\u00a0<\/em><br><br><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435. <\/strong>\u041f\u0440\u043e\u0432\u0435\u0434\u0435\u043c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u043d\u0430\u0434 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e\u043c. \u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \\(2x\\)<em> <\/em>\u0432 \u043b\u0435\u0432\u0443\u044e \u0447\u0430\u0441\u0442\u044c, \u0430 \\(\\frac{3a}{4}\\)<em> <\/em>\u2014 \u0432 \u043f\u0440\u0430\u0432\u0443\u044e:<br><br>\\(\\frac{x(a-2)}{a-1}-2x\\leq \\frac{3a}{4}-a\\)<br><br>\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:<br><br>\\(\\frac{ax-2x-2ax+2x}{a-1}\\leq -\\frac{a}{4}\\)<br><br>\u041f\u0440\u043e\u0432\u0435\u0434\u0435\u043c \u043f\u043e\u0434\u0441\u0447\u0435\u0442\u044b \u0432 \u043b\u0435\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0438:<br><br>\\(-\\frac{ax}{a-1}\\leq -\\frac{a}{4}\\)<br><br>\u0414\u043e\u043c\u043d\u043e\u0436\u0438\u043c \u043d\u0430 \\(-1\\). \u041f\u0440\u0438 \u044d\u0442\u043e\u043c \u0437\u043d\u0430\u043a \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u043d\u0430 \u043f\u0440\u043e\u0442\u0438\u0432\u043e\u043f\u043e\u043b\u043e\u0436\u043d\u044b\u0439:<br><br>\\(\\frac{a}{a-1}x\\geq \\frac{a}{4}\\)<br><br>\u041e\u0441\u0442\u0430\u0432\u0438\u043c <em>x <\/em>\u0432 \u043b\u0435\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0438, \u0430 \u0432\u0441\u0435 \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u043e\u0435 \u043f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \u0432 \u043f\u0440\u0430\u0432\u0443\u044e:<br><br>\\(x\\geq \\frac{a(a-1)}{4a}\\)<br>\\(x\\geq \\frac{a-1}{4}\\)<br><br>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0432\u0441\u0435 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0435 \u0441\u043b\u0443\u0447\u0430\u0438 \u0434\u043b\u044f <em>a<\/em>:<br><br>1) \u0415\u0441\u043b\u0438 \\(\\frac{a}{a-1}>0\\) \u0438\u043b\u0438 \\(a\\in (-\\infty; 0)\\cup (1;+\\infty)\\), \u0442\u043e\u0433\u0434\u0430 \\(x\\geq \\frac{a-1}{4}\\). \u041f\u0440\u043e\u0432\u0435\u0440\u0438\u043c \u044d\u0442\u043e \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435. \u0414\u043e\u043f\u0443\u0441\u0442\u0438\u043c, \\(a=2\\), \u0442\u043e\u0433\u0434\u0430:<br><br>\\(\\frac{2}{2-1}x\\geq \\frac{2}{4}\\)<br>\\(2x\\geq \\frac{1}{2}\\)<br>\\(2x\\geq \\frac{1}{2}\\)<br>\\(x\\geq \\frac{1}{4}\\)<br><br>\u0422\u043e \u0436\u0435 \u0441\u0430\u043c\u043e\u0435 \u043f\u043e\u043b\u0443\u0447\u0438\u043c, \u0435\u0441\u043b\u0438 \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u0438\u043c \\(a=2\\) \u0432 \\(x\\geq \\frac{a-1}{4}\\):<br><br>\\(x\\geq \\frac{2-1}{4}\\)<br>\\(x\\geq \\frac{1}{4}\\)<br><br>\u0421\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f. \u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u043c\u043e\u0436\u043d\u043e \u043f\u0440\u043e\u0432\u0435\u0440\u0438\u0442\u044c \u0438 \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u044b\u0435 \u0441\u043b\u0443\u0447\u0430\u0438.<br><br>2) \u0415\u0441\u043b\u0438 \\(\\frac{a}{a-1}=0\\) \u0438\u043b\u0438 \\(a=0\\), \u0442\u043e\u0433\u0434\u0430 <em>x<\/em> \u2014 \u043b\u044e\u0431\u043e\u0435 \u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e.<br>3) \u0415\u0441\u043b\u0438 \\(\\frac{a}{a-1}&lt;0\\) \u0438\u043b\u0438 \\(a\\in (0; 1)\\), \u0442\u043e\u0433\u0434\u0430 \\(x\\leq \\frac{a-1}{4}\\).\u00a0<br><br><strong>\u041e\u0442\u0432\u0435\u0442. <\/strong>\\(x\\in [\\frac{a-1}{4}; +\\infty]\\) \u043f\u0440\u0438 \\(a\\in (-\\infty; 0)\\cup (1; +\\infty); x\\in R\\) \u043f\u0440\u0438 \\(a = 0; x\\in [-\\infty; \\frac{a-1}{4}]\\) \u043f\u0440\u0438 \\(a\\in (0; 1)\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041a\u0430\u043a \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0437\u0430\u043c\u0435\u0442\u0438\u0442\u044c, \u0442\u0430\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0440\u0435\u0448\u0430\u044e\u0442\u0441\u044f \u043b\u0435\u0433\u043a\u043e, \u043d\u043e \u0432\u0430\u0436\u043d\u043e \u043d\u0435 \u0437\u0430\u0431\u044b\u0442\u044c \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0432\u0441\u0435 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0435 \u0441\u043b\u0443\u0447\u0430\u0438! \u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0441\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u043a \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u043c\u0443.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041f\u0440\u0438\u043c\u0435\u0440 1. <\/strong><em>\u0420\u0435\u0448\u0438\u0442\u044c \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e <\/em>\\((a-2)x > a^2-4\\)<em> \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 a.<\/em><strong><em>\u00a0<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0441\u043b\u0443\u0447\u0430\u0439, \u043a\u043e\u0433\u0434\u0430 \\(a = 2\\).<em> <\/em>\u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0432 \u043b\u0435\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0438 \u0431\u0443\u0434\u0435\u0442 \\(0 * x\\), \u0430 \u0432 \u043f\u0440\u0430\u0432\u043e\u0439 \u2014 <em>0<\/em>, \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(0*x>0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u0438 \u0442\u0430\u043a\u043e\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0438 <em>a <\/em>\u0443 <em>x <\/em>\u043d\u0435\u0442 \u0440\u0435\u0448\u0435\u043d\u0438\u0439.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0415\u0441\u043b\u0438 \u0436\u0435 \\(a > 2\\), \u0442\u043e\u0433\u0434\u0430 \u043e\u0441\u0442\u0430\u0432\u0438\u043c <em>x <\/em>\u0432 \u043b\u0435\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0438, \u0432\u0441\u0435 \u043e\u0441\u0442\u0430\u043b\u044c\u043d\u043e\u0435 \u043f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \u0432 \u043f\u0440\u0430\u0432\u0443\u044e \u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(x >\\frac{a^2-4}{a-2}\\). \u041f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0440\u0430\u0437\u043d\u043e\u0441\u0442\u0438 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 \\(a^2-b^2=(a-b)(a+b)\\):\u00a0<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(x >\\frac{(a-2)(a+2)}{a-2}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0418 \u0432 \u0447\u0438\u0441\u043b\u0438\u0442\u0435\u043b\u0435, \u0438 \u0432 \u0437\u043d\u0430\u043c\u0435\u043d\u0430\u0442\u0435\u043b\u0435 \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \\((a-2)\\), \u0437\u043d\u0430\u0447\u0438\u0442, \u043c\u043e\u0436\u0435\u043c \u0441\u043e\u043a\u0440\u0430\u0442\u0438\u0442\u044c:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(x > a+2\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u0438 \\(a &lt; 2\\) \u0431\u0443\u0434\u0435\u0442 \u0442\u043e \u0436\u0435 \u0441\u0430\u043c\u043e\u0435, \u043d\u043e \u0437\u043d\u0430\u043a \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f, \u0442\u0430\u043a \u043a\u0430\u043a \u043c\u044b \u0434\u0435\u043b\u0438\u043c \u043d\u0430 \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u0443\u044e \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(x &lt;\\frac{a^2-4}{a-2}\\) \u0438\u043b\u0438 \\(x &lt; a+2\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041e\u0442\u0432\u0435\u0442<\/strong>: \\(x\\notin R\\) \u043f\u0440\u0438 \\(a=2; x > a+2\\) \u043f\u0440\u0438 \\(a > 2; x &lt; a+2\\) \u043f\u0440\u0438 \\(a &lt; 2\\).<\/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\/2024\/02\/3-pravka-2-1024x708.png\" alt=\"\" class=\"wp-image-33976\" width=\"512\" height=\"354\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/3-pravka-2-1024x708.png 1024w, \/library\/wp-content\/uploads\/2024\/02\/3-pravka-2-300x207.png 300w, \/library\/wp-content\/uploads\/2024\/02\/3-pravka-2-768x531.png 768w, \/library\/wp-content\/uploads\/2024\/02\/3-pravka-2-1536x1062.png 1536w, \/library\/wp-content\/uploads\/2024\/02\/3-pravka-2.png 1866w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u043c\u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430\u043c\u0438 \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043b\u0438\u0441\u044c, \u0437\u0434\u0435\u0441\u044c \u0432\u0441\u0435 \u043e\u0447\u0435\u043d\u044c \u043b\u0435\u0433\u043a\u043e. \u041f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u043c \u043a \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u044b\u043c \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430\u043c.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u041a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u044b\u0435-\u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430-\u0441-\u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438\"><strong>\u041a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u044b\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u041e\u043d\u0438 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043d\u0435 \u043e\u0442\u043b\u0438\u0447\u0430\u044e\u0442\u0441\u044f \u043e\u0442 \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u0445, \u0442\u043e\u043b\u044c\u043a\u043e \u0442\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0434\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442 \u0438 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u0443 \u0434\u043b\u044f \u0430\u043d\u0430\u043b\u0438\u0437\u0430. \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u0440\u0430\u0437\u0431\u0435\u0440\u0435\u043c\u0441\u044f, \u043a\u0430\u043a \u044d\u0442\u043e \u0434\u0435\u043b\u0430\u0442\u044c.<\/p>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\u0420\u0435\u0448\u0438\u043c \u0437\u0430\u0434\u0430\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043c\u043e\u0436\u0435\u0442 \u043f\u043e\u043f\u0430\u0441\u0442\u044c\u0441\u044f \u043d\u0430 <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 \u211618.\u00a0<\/strong><br><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435. <\/strong><em>\u0420\u0435\u0448\u0438\u0442\u044c \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e <\/em>\\(ax^2-8x-16>0\\)<em> \u043f\u0440\u0438 \u0432\u0441\u0435\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 \u0430.<\/em><br><br><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435. <\/strong>\u0417\u0430\u043c\u0435\u0442\u0438\u043c, \u0447\u0442\u043e \u043f\u0440\u0438 \\(a = 0\\) \u043d\u0430\u0448\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u043f\u0440\u0435\u0432\u0440\u0430\u0449\u0430\u0435\u0442\u0441\u044f \u0432 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0435:<br><br>\\(-8x-16>0\\)<br>\\(x&lt; -2\\)<br><br>\u0415\u0441\u043b\u0438 \u0436\u0435 \\(a\\neq 0\\), \u0442\u043e \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0441\u0442\u0430\u043d\u043e\u0432\u0438\u0442\u0441\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u043c. \u041f\u043e\u0441\u0447\u0438\u0442\u0430\u0435\u043c \u0434\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442:<br><br>\\(D = 64+64a=64(1+a)\\)<\/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\/2024\/02\/4-27-1024x249.png\" alt=\"\" class=\"wp-image-33977\" width=\"512\" height=\"125\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/4-27-1024x249.png 1024w, \/library\/wp-content\/uploads\/2024\/02\/4-27-300x73.png 300w, \/library\/wp-content\/uploads\/2024\/02\/4-27-768x187.png 768w, \/library\/wp-content\/uploads\/2024\/02\/4-27-1536x374.png 1536w, \/library\/wp-content\/uploads\/2024\/02\/4-27-2048x499.png 2048w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\u0418\u043c\u0435\u0435\u043c: \u043f\u0440\u0438 \\(a&lt;-1\\) \u0434\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442 \\(D&lt;0; D=0\\) \u043f\u0440\u0438 \\(a=-1\\); \u043f\u0440\u0438 \\(a>-1\\) \u0434\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442 \\(D>0\\).<br><br>\u041d\u0430\u0439\u0434\u0435\u043c \u043a\u043e\u0440\u043d\u0438:<br>\\(x_1=\\frac{8+\\sqrt{64(1+a)}}{2a}\\)<br>\\(x_2=\\frac{4+\\sqrt{64(1-a)}}{2a}\\)<br><br>\\(x_1=\\frac{8+8\\sqrt{1+a}}{2a}\\)<br>\\(x_2=\\frac{8+8\\sqrt{64(1-a)}}{2a}\\)<br><br>\\(x_1=\\frac{4+4\\sqrt{1+a}}{a}\\)<br>\\(x_2=\\frac{4+4\\sqrt{64(1-a)}}{a}\\)<br><br>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0432\u0441\u0435 \u0441\u043b\u0443\u0447\u0430\u0438:<br><br>1) \\(a &lt; -1; D &lt; 0\\).<\/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\/2024\/02\/5-26-1024x335.png\" alt=\"\" class=\"wp-image-33978\" width=\"512\" height=\"168\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/5-26-1024x335.png 1024w, \/library\/wp-content\/uploads\/2024\/02\/5-26-300x98.png 300w, \/library\/wp-content\/uploads\/2024\/02\/5-26-768x251.png 768w, \/library\/wp-content\/uploads\/2024\/02\/5-26-1536x502.png 1536w, \/library\/wp-content\/uploads\/2024\/02\/5-26-2048x670.png 2048w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\u041f\u0430\u0440\u0430\u0431\u043e\u043b\u0430 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u0435\u0442 \u043e\u0441\u044c x, \u0438 \u044d\u0442\u043e \u0437\u043d\u0430\u0447\u0438\u0442, \u0447\u0442\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0439 \u043d\u0435\u0442. \u041f\u043e\u0434\u0440\u043e\u0431\u043d\u0435\u0435 \u043f\u0440\u043e \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u0443 \u0438 \u0432\u043b\u0438\u044f\u043d\u0438\u0438 \u043a\u043e\u044d\u0444\u0444\u0438\u0446\u0438\u0435\u043d\u0442\u043e\u0432 \u043d\u0430 \u0435\u0435 \u0432\u0438\u0434 \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0437\u043d\u0430\u0442\u044c \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 <a href=\"https:\/\/umschool.net\/library\/matematika\/osnovnye-elementarnye-funkczii-chast-2\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u00ab\u041e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438\u00bb<\/a>.<br><br>2) \\(a = -1; D = 0\\).<\/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\/2024\/02\/6-24-1024x279.png\" alt=\"\" class=\"wp-image-33980\" width=\"512\" height=\"140\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/6-24-1024x279.png 1024w, \/library\/wp-content\/uploads\/2024\/02\/6-24-300x82.png 300w, \/library\/wp-content\/uploads\/2024\/02\/6-24-768x209.png 768w, \/library\/wp-content\/uploads\/2024\/02\/6-24-1536x418.png 1536w, \/library\/wp-content\/uploads\/2024\/02\/6-24-2048x557.png 2048w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\u0422\u043e\u043b\u044c\u043a\u043e \u0432\u0435\u0440\u0448\u0438\u043d\u0430 \u043a\u0430\u0441\u0430\u0435\u0442\u0441\u044f \u043e\u0441\u0438 \\(x\\), \u043d\u043e \u043f\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u044e \u0437\u0430\u0434\u0430\u0447\u0438 \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \\(0\\) \u043d\u0435 \u043f\u043e\u0434\u0445\u043e\u0434\u0438\u0442.<br><br>3) \\(-1 &lt; a &lt; 0, D > 0\\). \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0432\u0435\u0442\u0432\u0438 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u044b \u0432\u043d\u0438\u0437, \u0437\u043d\u0430\u0447\u0438\u0442:<\/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\/2024\/02\/7-25-1024x444.png\" alt=\"\" class=\"wp-image-33981\" width=\"512\" height=\"222\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/7-25-1024x444.png 1024w, \/library\/wp-content\/uploads\/2024\/02\/7-25-300x130.png 300w, \/library\/wp-content\/uploads\/2024\/02\/7-25-768x333.png 768w, \/library\/wp-content\/uploads\/2024\/02\/7-25-1536x667.png 1536w, \/library\/wp-content\/uploads\/2024\/02\/7-25-2048x889.png 2048w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\u041c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u0435\u043d \u043f\u0440\u0438:<br><br>\\(x\\in (\\frac{4+4\\sqrt{1+a}}{a}; \\frac{4-4\\sqrt{1+a}}{a})\\)<br><br>\u0417\u0434\u0435\u0441\u044c \u0432\u0430\u0436\u043d\u043e \u043e\u0442\u043c\u0435\u0442\u0438\u0442\u044c, \u0447\u0442\u043e \\(\\frac{4+4\\sqrt{1+a}}{a}\\) \u043c\u0435\u043d\u044c\u0448\u0435, \u0442\u0430\u043a \u043a\u0430\u043a <em>a <\/em>\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0435\u0433\u043e \u0438 \u043d\u0430\u043f\u0438\u0441\u0430\u043b\u0438 \u043f\u0435\u0440\u0432\u044b\u043c.<br><br>4) \\(a > 0; D > 0\\).\u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0432\u0435\u0442\u0432\u0438 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u044b \u0432\u0432\u0435\u0440\u0445. \u041d\u0430\u0439\u0434\u0435\u043c \u043a\u043e\u0440\u043d\u0438:<br><br>\\(x_{1,2}=\\frac{8\\pm 8\\sqrt{1+a}}{2a}=\\frac{4\\pm 4\\sqrt{1+a}}{a}\\)<\/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\/2024\/02\/8-23-1024x444.png\" alt=\"\" class=\"wp-image-33982\" width=\"512\" height=\"222\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/8-23-1024x444.png 1024w, \/library\/wp-content\/uploads\/2024\/02\/8-23-300x130.png 300w, \/library\/wp-content\/uploads\/2024\/02\/8-23-768x333.png 768w, \/library\/wp-content\/uploads\/2024\/02\/8-23-1536x667.png 1536w, \/library\/wp-content\/uploads\/2024\/02\/8-23-2048x889.png 2048w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\u0421\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u043c\u043d\u043e\u0433\u043e\u0447\u043b\u0435\u043d \u0431\u0443\u0434\u0435\u0442 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u043f\u0440\u0438 \u0442\u0430\u043a\u043e\u043c \u0443\u0441\u043b\u043e\u0432\u0438\u0438:<br><br>\\(x\\in (-\\infty; \\frac{4-4\\sqrt{1+a}}{a})\\cup (\\frac{4+4\\sqrt{1+a}}{a};+\\infty)\\)<br><br>\u041c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u043b\u0438 \u0432\u0441\u0435 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0435 \u0441\u043b\u0443\u0447\u0430\u0438 \u0438 \u043c\u043e\u0436\u0435\u043c \u043d\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u043e\u0442\u0432\u0435\u0442.<br><br><strong>\u041e\u0442\u0432\u0435\u0442: <\/strong>\\(x&lt; -1\\) \u043f\u0440\u0438 \\(a = 0; x\\notin R\\) \u043f\u0440\u0438 \\(a\\leq -1; x\\in (\\frac{4+4\\sqrt{1+a}}{a}; \\frac{4-4\\sqrt{1+a}}{a})\\) \u043f\u0440\u0438 \\(-1 &lt; a &lt; 0; x\\in (-\\infty; \\frac{4-4\\sqrt{1+a}}{a})\\cup (\\frac{4+4\\sqrt{1+a}}{a};+\\infty)\\) \u043f\u0440\u0438 \\(a > 0\\).<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u0414\u043e\u043b\u0436\u0435\u043d \u043b\u0438 \u0431\u044b\u0442\u044c \u043e\u0442\u0432\u0435\u0442 \u0431\u044b\u0442\u044c \u043a\u0440\u0430\u0441\u0438\u0432\u044b\u043c \u0447\u0438\u0441\u043b\u043e\u043c?<\/strong><br><br>\u041a\u0430\u043a \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u0437\u0430\u043c\u0435\u0442\u0438\u0442\u044c, \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0441 \u043a\u043e\u0440\u043d\u044f\u043c\u0438 \u0438 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u0442\u0440\u0430\u0448\u043d\u044b\u043c\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u043c\u0438 \u0432\u0435\u0449\u0430\u043c\u0438 \u0432 \u0442\u0430\u043a\u0438\u0445 \u0437\u0430\u0434\u0430\u0447\u0430\u0445 \u0432\u043f\u043e\u043b\u043d\u0435 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u0435 \u0443\u0434\u0438\u0432\u043b\u044f\u0439\u0442\u0435\u0441\u044c \u043d\u0430 \u044d\u043a\u0437\u0430\u043c\u0435\u043d\u0435, \u0435\u0441\u043b\u0438 \u043f\u043e\u0441\u0447\u0438\u0442\u0430\u0435\u0442\u0435 \u0447\u0442\u043e-\u0442\u043e \u043f\u043e\u0434\u043e\u0431\u043d\u043e\u0435. \u0413\u043b\u0430\u0432\u043d\u043e\u0435 \u043f\u0435\u0440\u0435\u043f\u0440\u043e\u0432\u0435\u0440\u044f\u0439\u0442\u0435, \u0447\u0442\u043e\u0431\u044b \u0432\u0441\u0435 \u0442\u043e\u0447\u043d\u043e \u0431\u044b\u043b\u043e \u0440\u0435\u0448\u0435\u043d\u043e \u0432\u0435\u0440\u043d\u043e.<\/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\/2024\/02\/9-21-1016x1024.png\" alt=\"\" class=\"wp-image-33985\" width=\"254\" height=\"256\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/9-21-1016x1024.png 1016w, \/library\/wp-content\/uploads\/2024\/02\/9-21-298x300.png 298w, \/library\/wp-content\/uploads\/2024\/02\/9-21-150x150.png 150w, \/library\/wp-content\/uploads\/2024\/02\/9-21-768x774.png 768w, \/library\/wp-content\/uploads\/2024\/02\/9-21-1524x1536.png 1524w, \/library\/wp-content\/uploads\/2024\/02\/9-21.png 1800w\" sizes=\"auto, (max-width: 254px) 100vw, 254px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0443 \u0430 \u043c\u044b \u0438\u0434\u0435\u043c \u0434\u0430\u043b\u044c\u0448\u0435, \u043a \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u043c \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430\u043c \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c!<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u0418\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435-\u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430-\u0441-\u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438\"><strong>\u0418\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421\u0435\u0439\u0447\u0430\u0441 \u043c\u044b \u0437\u0430\u043c\u0435\u0442\u0438\u043c, \u0447\u0442\u043e \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043d\u0438\u0447\u0435\u0433\u043e \u043d\u043e\u0432\u043e\u0433\u043e \u044d\u0442\u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u043d\u0430\u043c \u043d\u0435 \u0434\u0430\u044e\u0442. \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041f\u0440\u0438\u043c\u0435\u0440 2. <\/strong>\u0420\u0435\u0448\u0438\u0442\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \\(5(2a+x)+9a\\sqrt{2a+x}>-2a^2\\) \u0434\u043b\u044f \u043b\u044e\u0431\u043e\u0433\u043e \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <em>a<\/em>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435.<\/strong> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \u0432\u0441\u0435 \u0432 \u043b\u0435\u0432\u0443\u044e \u0447\u0430\u0441\u0442\u044c:&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(5(2a+x)+9a\\sqrt{2a+x}-2a^2>0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0427\u0442\u043e \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0443\u0432\u0438\u0434\u0435\u0442\u044c \u0432 \u043b\u0435\u0432\u043e\u0439 \u0447\u0430\u0441\u0442\u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430? \u041f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e, \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u0442\u0440\u0435\u0445\u0447\u043b\u0435\u043d \u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e \\(\\sqrt{2a+x}\\). \u0417\u0430\u043c\u0435\u043d\u0438\u043c \\(\\sqrt{2a+x}\\) \u043d\u0430 \\(t\\), \u0442\u043e\u0433\u0434\u0430:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(5t^2+9at-2a^2>0\\)<br>\\(D = 81a^2+40a^2\\)<br>\\(t_{1,2}=\\frac{-9a\\pm \\sqrt{81a^2+40a^2}}{10}=\\frac{-9a\\pm 11a}{10}\\)<br>\\(t_1=\\frac{-9a+11a}{10}\\)<br>\\(t_2=\\frac{-9a-11a}{10}\\)<br>\\(t_1=\\frac{2a}{10}\\)<br>\\(t_2=\\frac{-20a}{10}\\)<br>\\(t_1=\\frac{a}{5}\\)<br>\\(t_2=-2a\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0420\u0430\u0437\u043b\u043e\u0436\u0438\u043c \u043b\u0435\u0432\u0443\u044e \u0447\u0430\u0441\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u0440\u0430\u0437\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u0442\u0440\u0435\u0445\u0447\u043b\u0435\u043d\u0430 \u043d\u0430 \u043c\u043d\u043e\u0436\u0438\u0442\u0435\u043b\u0438:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(5(\\sqrt{x+2a}+2a)(\\sqrt{x+2a}-\\frac{a}{5})>0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0441\u043b\u0443\u0447\u0430\u0439, \u043a\u043e\u0433\u0434\u0430 \\(a = 0\\):<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(5\\sqrt{x}*\\sqrt{x}>0\\)<br>\\(x>0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u043e\u043c\u0438\u043c\u043e \u044d\u0442\u043e\u0433\u043e, \u043f\u0440\u0438 \\(a &lt; 0\\) \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0432\u043e \u0432\u0442\u043e\u0440\u043e\u0439 \u0441\u043a\u043e\u0431\u043a\u0435 \\((\\sqrt{x+2a}-a5)\\) \u0431\u043e\u043b\u044c\u0448\u0435 \u043d\u0443\u043b\u044f. \u0417\u043d\u0430\u0447\u0438\u0442 \u043c\u043e\u0436\u043d\u043e \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0432 \u0442\u0430\u043a\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043f\u0435\u0440\u0435\u043f\u0438\u0441\u0430\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(\\sqrt{x+2a}+2a > 0\\)<br>\\(\\sqrt{x+2a} > -2a\\)<br>\\(x+2a > 4a^2\\)<br>\\(x>4a^2-2a\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0440\u0438 \\(\u0430 > 0\\)<em> <\/em>\u0432 \u043f\u0435\u0440\u0432\u043e\u0439 \u0441\u043a\u043e\u0431\u043a\u0435 \\((\\sqrt{x+2a}+2a)\\) \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0431\u0443\u0434\u0435\u0442 \u043f\u043e\u043b\u043e\u0436\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u043c, \u0437\u043d\u0430\u0447\u0438\u0442 \u043f\u0435\u0440\u0435\u043f\u0438\u0448\u0435\u043c \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0442\u0430\u043a:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(\\sqrt{x+2a}-\\frac{a}{5}>0\\)<br>\\(\\sqrt{x+2a}>\\frac{a}{5}\\)<br>\\(x+2a>\\frac{a^2}{25}\\)<br>\\(x>\\frac{a^2}{25}-2a\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u042d\u0442\u043e \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u0432\u0441\u0435 \u0437\u0430\u0434\u0430\u043d\u0438\u0435, \u043e\u0441\u0442\u0430\u043b\u043e\u0441\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0435: \\(a = 0\\) \u0432\u0445\u043e\u0434\u0438\u0442 \u0432 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0439 \u0441\u043b\u0443\u0447\u0430\u0439, \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u0437\u043d\u0430\u0435\u043c \u043e\u0442\u0432\u0435\u0442.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041e\u0442\u0432\u0435\u0442:<\/strong> \u043f\u0440\u0438 \\(a\\geq 0\\), \u0442\u043e \\(x>\\frac{a^2}{25}-2a\\); \u043f\u0440\u0438 \\(a &lt; 0\\), \u0442\u043e \\(x>4a^2-2a\\).\u00a0<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u041a\u043e\u0433\u0434\u0430 \u043f\u043e\u044f\u0432\u0438\u043b\u0438\u0441\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438?<\/strong><br><br>\u0417\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c \u0432\u0441\u0442\u0440\u0435\u0447\u0430\u043b\u0438\u0441\u044c \u0443\u0436\u0435 \u0432 \u0430\u0441\u0442\u0440\u043e\u043d\u043e\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u0442\u0440\u0430\u043a\u0442\u0430\u0442\u0435\u00ab\u0410\u0440\u0438\u0430\u0431\u0445\u0430\u0442\u0442\u0438\u0430\u043c\u00bb, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0431\u044b\u043b \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u0435\u043d \u0432 499 \u0433. \u0438\u043d\u0434\u0438\u0439\u0441\u043a\u0438\u043c \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u043e\u043c \u0438 \u0430\u0441\u0442\u0440\u043e\u043d\u043e\u043c\u043e\u043c \u0410\u0440\u0438\u0430\u0431\u0445\u0430\u0442\u0442\u043e\u0439. \u0414\u0440\u0443\u0433\u043e\u0439 \u0438\u043d\u0434\u0438\u0439\u0441\u043a\u0438\u0439 \u0443\u0447\u0435\u043d\u044b\u0439, \u0411\u0440\u0430\u0445\u043c\u0430\u0433\u0443\u043f\u0442\u0430, \u0432 7 \u0432\u0435\u043a\u0435 \u0438\u0437\u043b\u043e\u0436\u0438\u043b \u043e\u0431\u0449\u0435\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u043d\u044b\u0445 \u043a \u0435\u0434\u0438\u043d\u043e\u0439 \u043a\u0430\u043d\u043e\u043d\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u043e\u0440\u043c\u0435 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c: \\(ax^2+bx=c , a>0\\).<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421\u0443\u043f\u0435\u0440, \u043a\u043e\u0440\u043d\u0438 \u043f\u0440\u043e\u0448\u043b\u0438, \u0442\u0435\u043f\u0435\u0440\u044c \u043d\u0430 \u043f\u043e\u0434\u0445\u043e\u0434\u0435 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u044b!<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f-\u0438-\u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430-\u0441-\u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438,-\u0441\u043e\u0434\u0435\u0440\u0436\u0430\u0449\u0438\u0435-\u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u044b\"><strong>\u0423\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438, \u0441\u043e\u0434\u0435\u0440\u0436\u0430\u0449\u0438\u0435 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u044b<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><em>\u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0440\u0435\u0448\u0438\u043c \u0442\u0430\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435: <\/em>\\(log_4(16^x+a)=x\\)<em>. \u041d\u0443\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u0432\u0441\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 a, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0431\u0443\u0434\u0435\u0442 \u0438\u043c\u0435\u0442\u044c \u043e\u0434\u043d\u043e \u0438\u043b\u0438 \u0434\u0432\u0430 \u0440\u0435\u0448\u0435\u043d\u0438\u044f.<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412\u0441\u043f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c, \u0435\u0441\u043b\u0438 \u043f\u0440\u043e\u0441\u0442\u044b\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u2014 \u044d\u0442\u043e \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c \u0441\u0442\u0435\u043f\u0435\u043d\u0438. \u041f\u043e\u0434\u0440\u043e\u0431\u043d\u0435\u0435 \u043e \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430\u0445 \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u0440\u043e\u0447\u0435\u0441\u0442\u044c \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 <a href=\"https:\/\/umschool.net\/library\/matematika\/logarifmicheskie-uravneniya-i-neravenstva\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u00ab\u041b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430\u00bb<\/a>. \u0422\u043e \u0435\u0441\u0442\u044c \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u0442\u044c \u043d\u0430\u0448\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0430 \u0432 \u0434\u0440\u0443\u0433\u043e\u0435, \u043f\u043e\u043f\u0440\u043e\u0449\u0435:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(16^x+a=4^x\\)<br>\\(16^x-4^x+a=0\\)<br>\\(4^{2x}-4^x+a=0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u0443\u0441\u0442\u044c \\(t=4^x, t > 0\\), \u0442\u043e\u0433\u0434\u0430:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(t^2-t+a=0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u042d\u0442\u043e \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435. \u0427\u0442\u043e\u0431\u044b \u043e\u043d\u043e \u0438\u043c\u0435\u043b\u043e \u043e\u0434\u0438\u043d \u0438\u043b\u0438 \u0434\u0432\u0430 \u043a\u043e\u0440\u043d\u044f, \u043d\u0443\u0436\u043d\u043e, \u0447\u0442\u043e\u0431\u044b \u0434\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442 \u0431\u044b\u043b \u0431\u043e\u043b\u044c\u0448\u0435 \u0438\u043b\u0438 \u0440\u0430\u0432\u0435\u043d \\(0\\):<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(D = 1-4a\\geq 0\\)<br>\\(a\\leq \\frac{1}{4}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041e\u0442\u0432\u0435\u0442:<\/strong> \\(a\\leq \\frac{1}{4}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0440\u0435\u0448\u0430\u044e\u0442\u0441\u044f \u043f\u0440\u0438\u043c\u0435\u0440\u043d\u043e \u0442\u0430\u043a \u0436\u0435.\u00a0<\/p>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\">\u0420\u0435\u0448\u0438\u043c \u0437\u0430\u0434\u0430\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u043c\u043e\u0436\u0435\u0442 \u043f\u043e\u043f\u0430\u0441\u0442\u044c\u0441\u044f \u043d\u0430 <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 \u211618.\u00a0<\/strong><br><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435. <\/strong><em>\u041d\u0430\u0439\u0442\u0438 \u0432\u0441\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 <\/em>\\(b\\)<em>, \u043f\u0440\u0438 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 <\/em>\\(x=14\\) <em>\u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 <\/em>\\((x-14)(x-26)\\sqrt{b^2-24blog_{13}(x-13)-25}\\geq 0\\)<em>, \u0430 \u0447\u0438\u0441\u043b\u043e <\/em>\\(x=26\\)<em> \u043d\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f.<\/em><br><br><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435.<\/strong> \u041d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0440\u0430\u0432\u043d\u043e\u0441\u0438\u043b\u044c\u043d\u043e \u0441\u0438\u0441\u0442\u0435\u043c\u0435:<\/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\/2024\/02\/10-pravka-706x1024.png\" alt=\"\" class=\"wp-image-33989\" width=\"353\" height=\"512\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/10-pravka-706x1024.png 706w, \/library\/wp-content\/uploads\/2024\/02\/10-pravka-207x300.png 207w, \/library\/wp-content\/uploads\/2024\/02\/10-pravka-768x1114.png 768w, \/library\/wp-content\/uploads\/2024\/02\/10-pravka-1059x1536.png 1059w, \/library\/wp-content\/uploads\/2024\/02\/10-pravka-1411x2048.png 1411w, \/library\/wp-content\/uploads\/2024\/02\/10-pravka.png 1554w\" sizes=\"auto, (max-width: 353px) 100vw, 353px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background wp-block-paragraph\" style=\"background-color:#f0e5ff\"><strong>\u041e\u0442\u0432\u0435\u0442. <\/strong>\\(b\\in [5;25)\\)<\/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\/2024\/02\/11-15-971x1024.png\" alt=\"\" class=\"wp-image-33990\" width=\"308\" height=\"325\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/11-15-971x1024.png 971w, \/library\/wp-content\/uploads\/2024\/02\/11-15-285x300.png 285w, \/library\/wp-content\/uploads\/2024\/02\/11-15-768x810.png 768w, \/library\/wp-content\/uploads\/2024\/02\/11-15-1457x1536.png 1457w, \/library\/wp-content\/uploads\/2024\/02\/11-15.png 1591w\" sizes=\"auto, (max-width: 308px) 100vw, 308px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u0418\u0434\u0435\u043c \u0434\u0430\u043b\u044c\u0448\u0435, \u043a \u0437\u0430\u0434\u0430\u0447\u0430\u043c \u0441 \u0442\u0440\u0435\u0431\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f \u0438\u043b\u0438 \u043d\u0435\u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0434\u043b\u044f \u0432\u0441\u0435\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u0417\u0430\u0434\u0430\u0447\u0438-\u0441-\u0442\u0440\u0435\u0431\u043e\u0432\u0430\u043d\u0438\u0435\u043c-\u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f-(\u0438\u043b\u0438-\u043d\u0435\u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f)-\u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430-\u0434\u043b\u044f-\u0432\u0441\u0435\u0445-\u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439-\u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\"><strong>\u0417\u0430\u0434\u0430\u0447\u0438 \u0441 \u0442\u0440\u0435\u0431\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f (\u0438\u043b\u0438 \u043d\u0435\u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f) \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0434\u043b\u044f \u0432\u0441\u0435\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u041f\u043e\u0434\u043e\u0431\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043c\u044b \u0441\u0435\u0433\u043e\u0434\u043d\u044f \u0443\u0436\u0435 \u0440\u0435\u0448\u0430\u043b\u0438. \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0432 \u0440\u0430\u0437\u0434\u0435\u043b\u0435 \u043f\u0440\u043e \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u044b. \u0421\u0440\u0430\u0437\u0443 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0434\u0432\u0435 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043d\u0430 \u0441\u0435\u0433\u043e\u0434\u043d\u044f \u0438 \u0440\u0430\u0437\u0431\u0435\u0440\u0435\u043c\u0441\u044f, \u043a\u0430\u043a \u0440\u0435\u0448\u0430\u0442\u044c \u0442\u0430\u043a\u0438\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041f\u0440\u0438\u043c\u0435\u0440 3.<\/strong> \u0420\u0435\u0448\u0438\u0442\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \\(4ax+5cos(\\frac{\\pi}{3})\\geq 0\\) \u043f\u0440\u0438 \u0432\u0441\u0435\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 <em>a<\/em>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0412 \u0443\u0441\u043b\u043e\u0432\u0438\u0438 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 <a href=\"https:\/\/umschool.net\/library\/matematika\/trigonometricheskaya-okruzhnost-chast-2\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0442\u0430\u0431\u043b\u0438\u0447\u043d\u043e\u0435<\/a>, \u0430 \u0437\u043d\u0430\u0447\u0438\u0442 \u043e\u043d \u0440\u0430\u0432\u0435\u043d \\(\\frac{1}{2}\\). \u041f\u0435\u0440\u0435\u043d\u0435\u0441\u0435\u043c \u0432\u0441\u0435 \u0447\u0438\u0441\u043b\u0430 \u0432 \u043f\u0440\u0430\u0432\u0443\u044e \u0447\u0430\u0441\u0442\u044c:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(ax\\geq -\\frac{5}{8}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u0435\u043f\u0435\u0440\u044c \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0442\u0440\u0438 \u043f\u043e\u0442\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0441\u043b\u0443\u0447\u0430\u044f:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(a = 0\\), \u0432 \u0442\u0430\u043a\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0431\u0443\u0434\u0435\u0442 \u0432\u044b\u0433\u043b\u044f\u0434\u0435\u0442\u044c \u0442\u0430\u043a:<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(0\\geq -\\frac{5}{8}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u042d\u0442\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u0442\u0441\u044f \u043f\u0440\u0438 \u043b\u044e\u0431\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 <em>x<\/em>.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\"><li>\\(a &lt; 0\\), \u0442\u043e\u0433\u0434\u0430 \u043f\u0440\u0438 \u0434\u0435\u043b\u0435\u043d\u0438\u0438 \u043e\u0431\u0435\u0438\u0445 \u0447\u0430\u0441\u0442\u0435\u0439 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u043d\u0430 <em>a<\/em> \u0437\u043d\u0430\u043a \\(\\geq\\) \u0438\u0437\u043c\u0435\u043d\u0438\u0442\u0441\u044f \u043d\u0430 \\(\\leq\\). \u041f\u043e\u043b\u0443\u0447\u0438\u043c:<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(x\\leq -\\frac{5}{8a}\\)<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\"><li>\\(a > 0\\). \u041f\u043e\u0434\u0435\u043b\u0438\u043c \u043e\u0431\u0435 \u0447\u0430\u0441\u0442\u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u043d\u0430 <em>\u0430 <\/em>\u0438 \u043f\u043e\u043b\u0443\u0447\u0438\u043c:<\/li><\/ol>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(x\\geq -\\frac{5}{8a}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041e\u0442\u0432\u0435\u0442:<\/strong> \\(x\\in R\\) \u043f\u0440\u0438 \\(a = 0; x\\leq -\\frac{5}{8a}\\) \u043f\u0440\u0438 \\(a &lt; 0; x\\geq -\\frac{5}{8a}\\) \u043f\u0440\u0438 \\(a > 0\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0414\u0430, \u044d\u0442\u043e \u0431\u044b\u043b\u0430 \u043f\u0440\u0430\u0432\u0434\u0430 \u043b\u0435\u0433\u043a\u0430\u044f \u0437\u0430\u0434\u0430\u0447\u043a\u0430. \u0422\u0435\u043f\u0435\u0440\u044c \u0440\u0435\u0448\u0438\u043c \u0447\u0442\u043e-\u043d\u0438\u0431\u0443\u0434\u044c \u043f\u043e\u0441\u043b\u043e\u0436\u043d\u0435\u0435.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041f\u0440\u0438\u043c\u0435\u0440 4.<\/strong> \u0420\u0435\u0448\u0438\u0442\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \\(b(x^2-6)\\geq (2-3b^2)x\\) \u043f\u0440\u0438 \u0432\u0441\u0435\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 <em>b<\/em>.\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0432\u043e\u0442 \u0442\u0430\u043a:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(bx^2-6b-(2-3b^2)x\\geq 0\\)<br>\\(bx^2+(3b^2-2)x-6b\\geq 0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0427\u0442\u043e-\u0442\u043e \u043f\u043e\u0434\u043e\u0431\u043d\u043e\u0435 \u043c\u044b \u0441\u0435\u0433\u043e\u0434\u043d\u044f \u0443\u0436\u0435 \u0440\u0435\u0448\u0430\u043b\u0438. \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0441\u043b\u0443\u0447\u0430\u0439, \u043a\u043e\u0433\u0434\u0430 \\(b\\neq 0\\):<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(-2x\\geq 0\\)<br>\\(x\\leq 0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u0435\u043f\u0435\u0440\u044c \u043e\u0441\u0442\u0430\u043d\u043e\u0432\u0438\u043c\u0441\u044f \u043d\u0430 \u0441\u043b\u0443\u0447\u0430\u0435, \u043a\u043e\u0433\u0434\u0430 \\(b0\\). \u0412 \u0442\u0430\u043a\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0441\u0442\u0430\u043d\u0435\u0442 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u044b\u043c. \u0414\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(D = 9b^4-12b^2+24b^2=(3b^2+2)^2\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0414\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442 \u0431\u043e\u043b\u044c\u0448\u0435 \u043d\u0443\u043b\u044f, \u0442\u0430\u043a \u043a\u0430\u043a \u043e\u043d \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0435. \u0417\u043d\u0430\u0447\u0438\u0442, \u0447\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \\(bx^2+(3b^2-2)x-6b=0\\) \u0432\u0441\u0435\u0433\u0434\u0430 \u0438\u043c\u0435\u0435\u0442 \u0434\u0432\u0430 \u043a\u043e\u0440\u043d\u044f:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(x_1=-3b\\)<br>\\(x_2=\\frac{2}{b}\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0420\u0430\u0441\u043f\u0438\u0441\u0430\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u043e\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\u043c\u0438 \u043a\u043e\u0440\u043d\u044f\u043c\u0438 \u043c\u043e\u0436\u043d\u043e \u0442\u0430\u043a:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\(a(x-x_1)(x-x_2)\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0422\u043e\u0433\u0434\u0430 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c:<\/p>\n\n\n\n<p class=\"has-text-align-center wp-block-paragraph\">\\((bx-2)(x+3b)\\geq 0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0415\u0441\u043b\u0438 <em>b <\/em>\u043c\u0435\u043d\u044c\u0448\u0435 \u043d\u0443\u043b\u044f, \u0442\u043e \u0435\u0441\u0442\u044c \\(b &lt; 0\\), \u0442\u043e\u0433\u0434\u0430 \\(x_1>x_2\\) \u0438 \u0432\u0435\u0442\u0432\u0438 \u0443 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \\(y=(bx-2)(x+3b)\\geq 0\\) \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u044b \u0432\u043d\u0438\u0437:<\/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\/2024\/02\/12-16-1024x469.png\" alt=\"\" class=\"wp-image-33994\" width=\"512\" height=\"235\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/12-16-1024x469.png 1024w, \/library\/wp-content\/uploads\/2024\/02\/12-16-300x137.png 300w, \/library\/wp-content\/uploads\/2024\/02\/12-16-768x352.png 768w, \/library\/wp-content\/uploads\/2024\/02\/12-16-1536x704.png 1536w, \/library\/wp-content\/uploads\/2024\/02\/12-16-2048x938.png 2048w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0440\u0435\u0448\u0435\u043d\u0438\u0435\u043c \u0431\u0443\u0434\u0435\u0442 \\(x\\in [\\frac{2}{b};-3b]\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u0415\u0441\u043b\u0438 \u0436\u0435\u00a0\\(b > 0\\), \u0442\u043e\u0433\u0434\u0430 \\(x_1&lt;x_2\\) \u0438 \u0432\u0435\u0442\u0432\u0438 \u0443 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \\(y=(bx-2)(x+3b)\\geq 0\\) \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u044b \u0432\u0432\u0435\u0440\u0445:<\/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\/2024\/02\/13-16-1024x436.png\" alt=\"\" class=\"wp-image-33995\" width=\"512\" height=\"218\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/13-16-1024x436.png 1024w, \/library\/wp-content\/uploads\/2024\/02\/13-16-300x128.png 300w, \/library\/wp-content\/uploads\/2024\/02\/13-16-768x327.png 768w, \/library\/wp-content\/uploads\/2024\/02\/13-16-1536x654.png 1536w, \/library\/wp-content\/uploads\/2024\/02\/13-16-2048x872.png 2048w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u0410 \u044d\u0442\u043e \u0437\u043d\u0430\u0447\u0438\u0442, \u0447\u0442\u043e \u0440\u0435\u0448\u0435\u043d\u0438\u0435: \\(x\\in (-\\infty; -3b]\\cup [\\frac{2}{b};+\\infty)\\).\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041e\u0442\u0432\u0435\u0442: <\/strong>\\(x\\leq 0\\) \u043f\u0440\u0438 \\(b=0; x\\in (-\\infty; -3b]\\cup [\\frac{2}{b};+\\infty)\\) \u043f\u0440\u0438 \\(b>0; x\\in [\\frac{2}{b};-3a]\\) \u043f\u0440\u0438 \\(b&lt;0\\).<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u041f\u0430\u0440\u0430\u0431\u043e\u043b\u0430: \u043a\u0430\u043a \u043e\u043d\u0430 \u043f\u043e\u043c\u043e\u0436\u0435\u0442 \u0432\u0430\u043c \u043d\u0430 \u0415\u0413\u042d?<\/strong><br><br>\u0421\u0435\u0433\u043e\u0434\u043d\u044f \u043c\u044b \u0432\u0438\u0434\u0435\u043b\u0438 \u0434\u0432\u0430 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438, \u0432 \u0440\u0435\u0448\u0435\u043d\u0438\u0438 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043d\u0430\u043c \u043e\u0447\u0435\u043d\u044c \u043f\u043e\u043c\u043e\u0433\u043b\u0430 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u0430. \u0423 \u043d\u0435\u0435 \u0435\u0441\u0442\u044c \u0442\u0430\u043a\u0438\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u043e\u043c\u043e\u0433\u0430\u044e\u0442 \u0440\u0435\u0448\u0430\u0442\u044c \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438.<\/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\/2024\/02\/14-12-998x1024.png\" alt=\"\" class=\"wp-image-33996\" width=\"250\" height=\"256\" srcset=\"\/library\/wp-content\/uploads\/2024\/02\/14-12-998x1024.png 998w, \/library\/wp-content\/uploads\/2024\/02\/14-12-292x300.png 292w, \/library\/wp-content\/uploads\/2024\/02\/14-12-768x788.png 768w, \/library\/wp-content\/uploads\/2024\/02\/14-12.png 1359w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">\u041d\u0430 \u044d\u0442\u043e\u043c \u043d\u0430\u0448\u0435 \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438 \u043e\u043a\u043e\u043d\u0447\u0435\u043d\u043e. \u0422\u0435\u043f\u0435\u0440\u044c \u0432\u044b \u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u0440\u0435\u0448\u0430\u0442\u044c \u0438\u0445, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0437\u0430 \u043d\u0438\u0445 \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0431\u0430\u043b\u043b \u043d\u0430 \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! \u0410 \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0430\u0442\u044c \u043c\u0430\u043a\u0441\u0438\u043c\u0430\u043b\u044c\u043d\u044b\u0439 \u0431\u0430\u043b\u043b \u0437\u0430 \u0434\u0440\u0443\u0433\u0438\u0435 \u0437\u0430\u0434\u0430\u043d\u0438\u044f, \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u0440\u043e\u0447\u0438\u0442\u0430\u0442\u044c \u0441\u0442\u0430\u0442\u044c\u044e <a href=\"https:\/\/umschool.net\/library\/matematika\/tekstovye-zadachi\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u00ab\u0422\u0435\u043a\u0441\u0442\u043e\u0432\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438\u00bb<\/a>.<\/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 class=\"wp-block-paragraph\"><strong>\u0414\u0438\u0441\u043a\u0440\u0438\u043c\u0438\u043d\u0430\u043d\u0442 \u0432 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u043c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0438<\/strong> \u2014 \u044d\u0442\u043e \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0438\u0449\u0435\u0442\u0441\u044f \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \\(D=b^2-4ac\\), \u0433\u0434\u0435 <em>\u0430<\/em>, <em>b<\/em> \u0438 <em>\u0441<\/em> \u0431\u0435\u0440\u0443\u0442\u0441\u044f \u0438\u0437 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041f\u0430\u0440\u0430\u0431\u043e\u043b\u0430<\/strong> \u2014 \u044d\u0442\u043e \u043d\u0435\u0437\u0430\u043c\u043a\u043d\u0443\u0442\u0430\u044f \u043b\u0438\u043d\u0438\u044f, \u0442\u043e\u0447\u043a\u0438 \u043d\u0430 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u0440\u0430\u0432\u043d\u043e\u0443\u0434\u0430\u043b\u0435\u043d\u044b \u043e\u0442 \u043e\u0441\u0438 \u0441\u0438\u043c\u043c\u0435\u0442\u0440\u0438\u0438.<\/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>\u0412 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430\u0445 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c \u0432\u0430\u0436\u043d\u043e \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0432\u0441\u0435 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u044b\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 <em>a.<\/em><\/li><li>\u0412 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u0438\u0447\u043d\u044b\u0445 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430\u0445 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c \u0434\u043b\u044f \u0430\u043d\u0430\u043b\u0438\u0437\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u0443.<\/li><li>\u041e\u0442\u0432\u0435\u0442\u044b \u0441 \u043a\u043e\u0440\u043d\u044f\u043c\u0438 \u2014 \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e\u0435 \u044f\u0432\u043b\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u0437\u0430\u0434\u0430\u043d\u0438\u044f.<\/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 class=\"wp-block-paragraph\"><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 1.<\/strong><br>\u0427\u0442\u043e \u0437\u043d\u0430\u0447\u0438\u0442 \u00ab\u0420\u0435\u0448\u0438\u0442\u044c \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u043e\u043c\u00bb?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\u041d\u0430\u0439\u0442\u0438 \u041e\u0414\u0417 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 <em>\u0430.<\/em><\/li><li>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u043f\u0440\u0438 \u043a\u0430\u043a\u0438\u0445 <em>x<\/em> \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440 <em>a.<\/em><\/li><li>\u041d\u0430\u0439\u0442\u0438 \u0432\u0441\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 <em>a <\/em>\u043f\u0440\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 <em>x.<\/em><\/li><li>\u041d\u0430\u0439\u0442\u0438 \u0432\u0441\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f <em>x<\/em> \u043f\u0440\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 <em>a.<\/em><\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 2.<\/strong><br>\u041f\u0440\u0438 \u043a\u0430\u043a\u0438\u0445 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f\u0445 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430 <em>\u0430 <\/em>\u0432\u0435\u0442\u0432\u0438 \u043f\u0430\u0440\u0430\u0431\u043e\u043b\u044b \u0431\u0443\u0434\u0443\u0442 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u044b \u0432\u043d\u0438\u0437 \u0443 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \\(ax^2-4x-20>0\\)?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(a > 0\\)<\/li><li>\\(a = 1\\)<\/li><li>\\(a &lt; 0\\)<\/li><li>\\(a = 0\\)<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 3.<\/strong><br>\u041a\u0430\u043a \u0440\u0435\u0448\u0438\u0442\u044c \u0434\u0430\u043d\u043d\u043e\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e:\u00a0\\(10(4a-x)+15a\\sqrt{4a-x}-5a>0\\)?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\u041a\u0430\u043a \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e.<\/li><li>\u0421 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0437\u0430\u043c\u0435\u043d\u044b \\(t = 4a\\).<\/li><li>\u041a\u0430\u043a \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u0439 \u0442\u0440\u0435\u0445\u0447\u043b\u0435\u043d.<\/li><li>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0432\u0441\u0435 \u0441\u043b\u0443\u0447\u0430\u0438, \u043a\u043e\u0433\u0434\u0430 \u043a\u043e\u0440\u0435\u043d\u044c \u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u0435\u043d.<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 4.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u041a\u0430\u043a\u0438\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u044f \u043f\u0440\u0438\u043d\u0438\u043c\u0430\u0435\u0442 <em>x<\/em> \u043f\u0440\u0438 \\(a = 0\\) \u0432 \u0434\u0430\u043d\u043d\u043e\u043c \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0435: \\(ax &lt; -1\\)?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(x\\notin R\\).<\/li><li>\\(x\\in R\\).<\/li><li>\\(x > 0\\).<\/li><li>\\(x = 0\\).<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u041e\u0442\u0432\u0435\u0442\u044b<\/strong>: <strong>1. \u2014 <\/strong>4;<strong> 2. \u2014 <\/strong>3;<strong> 3. \u2014 <\/strong>3;<strong> 4. \u2014 <\/strong>1.<\/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 \u0414\u043e\u043b\u0436\u0435\u043d \u043b\u0438 \u043e\u0442\u0432\u0435\u0442 \u0431\u044b\u0442\u044c \u043a\u0440\u0430\u0441\u0438\u0432\u044b\u043c \u0447\u0438\u0441\u043b\u043e\u043c? \u041a\u043e\u0433\u0434\u0430 \u043f\u043e\u044f\u0432\u0438\u043b\u0438\u0441\u044c \u043f\u0440\u0438\u043c\u0435\u0440\u044b \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438? \u041f\u0430\u0440\u0430\u0431\u043e\u043b\u0430: \u043a\u0430\u043a \u043e\u043d\u0430 \u043f\u043e\u043c\u043e\u0436\u0435\u0442 \u0432\u0430\u043c \u043d\u0430 \u0415\u0413\u042d? \u041f\u0440\u0435\u0434\u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0435 \u0437\u0430\u0434\u0430\u043d\u0438\u0435 \u0432 \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. \u0412\u043e\u0437\u043c\u043e\u0436\u043d\u043e, \u0441\u0430\u043c\u043e\u0435 \u0441\u043b\u043e\u0436\u043d\u043e\u0435. \u041d\u043e \u0442\u0430\u043a \u043b\u0438 \u043e\u043d\u043e \u043f\u0443\u0433\u0430\u044e\u0449\u0435, \u043a\u0430\u043a \u043e \u043d\u0435\u043c \u0433\u043e\u0432\u043e\u0440\u044f\u0442? \u0423\u0437\u043d\u0430\u0435\u043c \u043e\u0431 \u044d\u0442\u043e\u043c \u0432 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435! \u041b\u0438\u043d\u0435\u0439\u043d\u044b\u0435 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0438 \u043d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430, \u043f\u0440\u0438\u0432\u043e\u0434\u0438\u043c\u044b\u0435 \u043a \u043b\u0438\u043d\u0435\u0439\u043d\u044b\u043c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":37416,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[22],"tags":[1414],"class_list":["post-33965","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-parametry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u041d\u0435\u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u0430 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438 - \u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a<\/title>\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\/neravenstva-s-parametrami\/\" 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