{"id":35622,"date":"2024-03-11T16:49:21","date_gmt":"2024-03-11T16:49:21","guid":{"rendered":"https:\/\/umschool.net\/library\/?p=35622"},"modified":"2024-03-11T16:51:55","modified_gmt":"2024-03-11T16:51:55","slug":"geometricheskie-zadachi-s-elementami-algebry-i-naoborot","status":"publish","type":"post","link":"https:\/\/umschool.net\/library\/matematika\/geometricheskie-zadachi-s-elementami-algebry-i-naoborot\/","title":{"rendered":"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u044b \u0438 \u043d\u0430\u043e\u0431\u043e\u0440\u043e\u0442"},"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>\u0427\u0442\u043e \u043f\u043e\u044f\u0432\u0438\u043b\u043e\u0441\u044c \u043f\u0435\u0440\u0432\u0435\u0435: \u0430\u043b\u0433\u0435\u0431\u0440\u0430 \u0438\u043b\u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f?<\/li><li>\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0438\u0444\u0430\u0433\u043e\u0440\u043e\u0432\u044b \u0442\u0440\u043e\u0439\u043a\u0438 \u0438 \u043a\u0430\u043a \u0438\u0445 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c?<\/li><li>\u041a\u0430\u043a \u0440\u0430\u0437\u0440\u0435\u0437\u0430\u0442\u044c \u0442\u043e\u0440\u0442 \u043d\u0430 8 \u043a\u0443\u0441\u043a\u043e\u0432 \u0437\u0430 \u0442\u0440\u0438 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f?<\/li><\/ul>\n\n\n\n<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0441 \u0432\u0430\u043c\u0438 \u0443\u0437\u043d\u0430\u0435\u043c \u043f\u0430\u0440\u043e\u0447\u043a\u0443 \u043b\u0430\u0439\u0444\u0445\u0430\u043a\u043e\u0432, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u043e\u043c\u043e\u0433\u0443\u0442 \u0440\u0435\u0448\u0430\u0442\u044c \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0430\u043b\u0433\u0435\u0431\u0440\u044b, \u0430 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u2014 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438. \u041f\u0440\u0438\u0441\u0442\u0443\u043f\u0438\u043c!<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435-\u0437\u0430\u0434\u0430\u0447\u0438-\u0441-\u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c\u0438-\u0430\u043b\u0433\u0435\u0431\u0440\u044b\"><strong>\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u044b<\/strong><\/h2>\n\n\n\n<p>\u041d\u0430\u0447\u043d\u0435\u043c \u0441 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0437\u0430\u0434\u0430\u0447. \u0418\u043d\u043e\u0433\u0434\u0430 \u043e\u043d\u0438 \u043a\u0430\u0436\u0443\u0442\u0441\u044f \u0441\u043b\u043e\u0436\u043d\u0435\u0435, \u043d\u0435\u0436\u0435\u043b\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0441\u0435\u0439\u0447\u0430\u0441 \u043c\u044b \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c, \u043a\u0430\u043a \u0438\u0445 \u043c\u043e\u0436\u043d\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0430\u043b\u0433\u0435\u0431\u0440\u044b.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>\u0427\u0442\u043e \u043f\u043e\u044f\u0432\u0438\u043b\u043e\u0441\u044c \u043f\u0435\u0440\u0432\u0435\u0435: \u0430\u043b\u0433\u0435\u0431\u0440\u0430 \u0438\u043b\u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f?<\/strong><br><br>\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u043f\u043e\u044f\u0432\u0438\u043b\u0430\u0441\u044c \u0440\u0430\u043d\u044c\u0448\u0435, \u0447\u0435\u043c \u0430\u043b\u0433\u0435\u0431\u0440\u0430. \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f \u0437\u0430\u043d\u0438\u043c\u0430\u043b\u0430\u0441\u044c \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u0435\u043c \u0444\u043e\u0440\u043c \u0438 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0430 \u0435\u0449\u0435 \u0432 \u0434\u0440\u0435\u0432\u043d\u0438\u0445 \u0446\u0438\u0432\u0438\u043b\u0438\u0437\u0430\u0446\u0438\u044f\u0445, \u0442\u0430\u043a\u0438\u0445 \u043a\u0430\u043a \u0415\u0433\u0438\u043f\u0435\u0442 \u0438 \u0412\u0430\u0432\u0438\u043b\u043e\u043d. \u0410\u043b\u0433\u0435\u0431\u0440\u0430 \u0432\u043e\u0437\u043d\u0438\u043a\u043b\u0430 \u043f\u043e\u0437\u0436\u0435, \u0432 3 \u0432\u0435\u043a\u0435 \u0434\u043e \u043d.\u044d., \u043a\u043e\u0433\u0434\u0430 \u0414\u0438\u043e\u0444\u0430\u043d\u0442 \u0438\u0437 \u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440\u0438\u0438 \u043d\u0430\u043f\u0438\u0441\u0430\u043b \u043f\u0435\u0440\u0432\u044b\u0439 \u0442\u0440\u0430\u043a\u0442\u0430\u0442 \u043f\u043e \u0430\u043b\u0433\u0435\u0431\u0440\u0435.\u00a0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u041d\u0430\u0447\u043d\u0435\u043c \u0441\u0440\u0430\u0437\u0443 \u0441 \u043f\u0440\u0438\u043c\u0435\u0440\u0430 \u0442\u0430\u043a\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0438 \u0438\u0437 \u0415\u0413\u042d.<\/p>\n\n\n\n<p class=\"has-background\" 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 \u21161.\u00a0<\/strong><br><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435. <\/strong><em>\u0414\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u0438 \u0440\u043e\u043c\u0431\u0430 \u043e\u0442\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u043a\u0430\u043a 3:4. \u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u0440\u043e\u043c\u0431\u0430 \u0440\u0430\u0432\u0435\u043d 400. \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0432\u044b\u0441\u043e\u0442\u0443 \u0440\u043e\u043c\u0431\u0430.\u00a0<\/em><br><br><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435.<\/strong> \u041f\u0443\u0441\u0442\u044c \u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u0438 \u0440\u043e\u043c\u0431\u0430 \u0440\u0430\u0432\u043d\u044b \\(6\u0445\\) \u0438 \\(8\u0445\\), \u0442\u0430\u043a \u043a\u0430\u043a \u043c\u043e\u0436\u043d\u043e \u0441\u043e\u0441\u0442\u0430\u0432\u0438\u0442\u044c <a href=\"https:\/\/umschool.net\/library\/matematika\/finansovye-zadachi-proczenty\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u043f\u0440\u043e\u043f\u043e\u0440\u0446\u0438\u044e<\/a> \\(6x:8x=3:4\\). \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u044b\u0439 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a ABO. \u0412 \u043d\u0435\u043c \u043f\u043e \u0442\u0435\u043e\u0440\u0435\u043c\u0435 \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430 \u043d\u0430\u0439\u0434\u0435\u043c \u0433\u0438\u043f\u043e\u0442\u0435\u043d\u0443\u0437\u0443 AB.<\/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\/03\/1-1024x620.png\" alt=\"\" class=\"wp-image-35628\" width=\"256\" height=\"155\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/1-1024x620.png 1024w, \/library\/wp-content\/uploads\/2024\/03\/1-300x182.png 300w, \/library\/wp-content\/uploads\/2024\/03\/1-768x465.png 768w, \/library\/wp-content\/uploads\/2024\/03\/1-1536x931.png 1536w, \/library\/wp-content\/uploads\/2024\/03\/1.png 1682w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\">\\(AB^2=AO^2+OB^2\\)<br>\\(AB^2=9x^2+16x^2\\)<br>\\(AB^2=25x^2\\)<br>\\(AB = 5x\\)<br><br>\u0422\u0430\u043a \u043a\u0430\u043a \\(P = 400\\), \u0442\u043e:<br><br>\\(5x*4=400\\)<br>\\(x=20\\)<br><br>\u0422\u043e\u0433\u0434\u0430 AB:<br><br>\\(AB=5*20=100\\)<br><br>\u0410 \u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u0438 \u0440\u0430\u0432\u043d\u044b:<br><br>\\(6x=120\\)<br>\\(8x=160\\)<br><br>\u0422\u0435\u043f\u0435\u0440\u044c, \u0447\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0432\u044b\u0441\u043e\u0442\u0443, \u043c\u043e\u0436\u0435\u043c \u0432\u043e\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c\u0441\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0430\u043c\u0438 \u043f\u043b\u043e\u0449\u0430\u0434\u0438 \u0440\u043e\u043c\u0431\u0430:<br><br>\\(S=\\frac{1}{2}*d_1*d_2\\)<br>\\(S=ah\\)<br>\\(\\frac{1}{2}*d_1*d_2=ah\\)<br>\\(\\frac{1}{2}*120*160=100*h\\)<br>\\(h=96\\)<br><br><strong>\u041e\u0442\u0432\u0435\u0442: <\/strong>\\(96\\)<\/p>\n\n\n\n<p>\u041a\u0430\u043a \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0437\u0430\u043c\u0435\u0442\u0438\u0442\u044c, \u043c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043b\u0438 \u043c\u043d\u043e\u0433\u043e \u0444\u043e\u0440\u043c\u0443\u043b, \u0432 \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e\u0441\u0442\u0438 \u0444\u043e\u0440\u043c\u0443\u043b\u044b \u043f\u043b\u043e\u0449\u0430\u0434\u0438. \u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0444\u043e\u0440\u043c\u0443\u043b \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043c\u0435\u0442\u043e\u0434\u043e\u043c \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439.&nbsp;<\/p>\n\n\n\n<p>\u041c\u0435\u0442\u043e\u0434 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u0438 \u043c\u0435\u0442\u043e\u0434 \u043e\u0431\u044a\u0435\u043c\u043e\u0432 \u043c\u044b \u0440\u0430\u0437\u0431\u0438\u0440\u0430\u043b\u0438 \u0432 \u0434\u0440\u0443\u0433\u043e\u0439 \u043d\u0430\u0448\u0435\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u2014 \u00ab\u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440, \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0438 \u043e\u0431\u044a\u0435\u043c\u00bb. \u042d\u0442\u0438 \u043c\u0435\u0442\u043e\u0434\u044b \u043f\u043e\u043c\u043e\u0433\u0430\u044e\u0442 \u0440\u0435\u0448\u0438\u0442\u044c \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0430\u043b\u0433\u0435\u0431\u0440\u044b.<\/p>\n\n\n\n<p>\u041f\u043e\u043c\u0438\u043c\u043e \u044d\u0442\u043e\u0433\u043e, \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 \u0442\u043e\u0436\u0435 \u043c\u043e\u0436\u043d\u043e \u0440\u0435\u0448\u0430\u0442\u044c \u043d\u0435 \u0442\u043e\u043b\u044c\u043a\u043e \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438, \u043d\u043e \u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438.&nbsp;<\/p>\n\n\n\n<p><strong>\u041f\u0440\u0438\u043c\u0435\u0440 1<\/strong>. \u041f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b \u043b\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \\(a=\\{1, 5, -2\\}, b=\\{3, -1, 9\\}\\)?<\/p>\n\n\n\n<p><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435.<\/strong> \u041d\u0435 \u0431\u0443\u0434\u0435\u043c \u0441\u0442\u0440\u043e\u0438\u0442\u044c \u044d\u0442\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u044b, \u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u0430\u043b\u0433\u0435\u0431\u0440\u0443. \u0412\u0435\u043a\u0442\u043e\u0440\u044b \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b, \u0435\u0441\u043b\u0438 \u0438\u0445 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u043b\u044e. \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0442\u0430\u043a:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(\\vec{a}*\\vec{b}=x_1x_2+y_1y_2+z_1z_2\\)<\/p>\n\n\n\n<p>\u041f\u043e\u0441\u0447\u0438\u0442\u0430\u0435\u043c \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 <em>a <\/em>\u0438 <em>b:<\/em><\/p>\n\n\n\n<p class=\"has-text-align-center\">\\(\\vec{a}*\\vec{b}=1*3+5*(-1)+(-2)*9=-20\\neq 0\\)<\/p>\n\n\n\n<p>\u0420\u0430\u0437 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043d\u0435 \u0440\u0430\u0432\u043d\u043e 0, \u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u043d\u0435 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b.&nbsp;<\/p>\n\n\n\n<p><strong>\u041e\u0442\u0432\u0435\u0442:<\/strong> \u043d\u0435 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\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\/2024\/03\/image-350-1024x829.png\" alt=\"\" class=\"wp-image-35630\" width=\"512\" height=\"415\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/image-350-1024x829.png 1024w, \/library\/wp-content\/uploads\/2024\/03\/image-350-300x243.png 300w, \/library\/wp-content\/uploads\/2024\/03\/image-350-768x622.png 768w, \/library\/wp-content\/uploads\/2024\/03\/image-350-1536x1243.png 1536w, \/library\/wp-content\/uploads\/2024\/03\/image-350.png 1600w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p>\u0421 \u043f\u0440\u0438\u043c\u0435\u0440\u0430\u043c\u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0437\u0430\u0434\u0430\u0447, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u043e\u0436\u043d\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0430\u043b\u0433\u0435\u0431\u0440\u044b, \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043b\u0438\u0441\u044c. \u0422\u0435\u043f\u0435\u0440\u044c \u043c\u043e\u0436\u0435\u043c \u043f\u0435\u0440\u0435\u0445\u043e\u0434\u0438\u0442\u044c \u043a \u0437\u0430\u0434\u0430\u0447\u0430\u043c \u0430\u043b\u0433\u0435\u0431\u0440\u044b \u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438.<\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"\u0417\u0430\u0434\u0430\u0447\u0438-\u0430\u043b\u0433\u0435\u0431\u0440\u044b-\u0441-\u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c-\u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438\"><strong>\u0417\u0430\u0434\u0430\u0447\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u044b \u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438<\/strong><\/h2>\n\n\n\n<p>\u0425\u043e\u0442\u044c \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u043d\u0438\u044f \u0438 \u043b\u0435\u0433\u0447\u0435, \u0447\u0435\u043c \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435, \u0438\u0445 \u0432\u0441\u0435 \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u0436\u043d\u043e \u0443\u043c\u0435\u0442\u044c \u0440\u0435\u0448\u0430\u0442\u044c \u0440\u0430\u0437\u043d\u044b\u043c\u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u0430\u043c\u0438, \u0447\u0442\u043e\u0431\u044b \u0442\u043e\u0447\u043d\u043e \u0431\u044b\u0442\u044c \u0443\u0432\u0435\u0440\u0435\u043d\u043d\u044b\u043c \u0432 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u043e\u043c \u043e\u0442\u0432\u0435\u0442\u0435.&nbsp;<\/p>\n\n\n\n<p>\u041f\u0435\u0440\u0435\u0439\u0434\u0435\u043c \u043a \u043f\u0440\u0438\u043c\u0435\u0440\u0443, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c, \u043a\u0430\u043a \u043c\u043e\u0436\u043d\u043e \u0440\u0435\u0448\u0430\u0442\u044c \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438.<\/p>\n\n\n\n<p class=\"has-background\" 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 \u21166.\u00a0<\/strong><br><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435. <\/strong><em>\u0420\u0435\u0448\u0438\u0442\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 <\/em>\\(\\sqrt{64+x^2}=10\\)<em>. \u0412 \u043e\u0442\u0432\u0435\u0442 \u0437\u0430\u043f\u0438\u0448\u0438\u0442\u0435 \u0431\u043e\u043b\u044c\u0448\u0438\u0439 \u0438\u0437 \u043a\u043e\u0440\u043d\u0435\u0439.<\/em><br><br><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435.<\/strong> \u0410\u0431\u0441\u0442\u0440\u0430\u0433\u0438\u0440\u0443\u0435\u043c\u0441\u044f \u043e\u0442 \u0442\u043e\u0433\u043e, \u0447\u0442\u043e \u044d\u0442\u043e \u2014 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435. \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u044b\u0439 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a, \u0443 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0433\u0438\u043f\u043e\u0442\u0435\u043d\u0443\u0437\u0430 \u0440\u0430\u0432\u043d\u0430 10, \u043e\u0434\u0438\u043d \u043a\u0430\u0442\u0435\u0442 \u0440\u0430\u0432\u0435\u043d 8, \u0430 \u0432\u0442\u043e\u0440\u043e\u0439 \u2014 <em>\u0445<\/em>. \u0422\u043e\u0433\u0434\u0430 \u043f\u043e\u043b\u0443\u0447\u0438\u043c \u043e\u0431\u044b\u0447\u043d\u0443\u044e <a href=\"https:\/\/umschool.net\/library\/matematika\/ravnobedrennyj-ravnostoronnij-i-pryamougolnyj-treugolnik\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0442\u0435\u043e\u0440\u0435\u043c\u0443 \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430<\/a>. \u0421\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u043f\u043e\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u043c \u0447\u0438\u0441\u043b\u0430 \u0432 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0442\u0435\u043e\u0440\u0435\u043c\u0443 \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430:<br><br>\\(10^2=8^2+x^2\\)<br>\\(100 = 64+x^2\\)<br>\\(x^2=36\\)<br>\\(x=\\pm 6\\)<br><br>\u0421\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u043a\u043e\u0440\u043d\u0438 \u0440\u0430\u0432\u043d\u044b \\(x=\\pm 6\\). \u0422\u0430\u043a \u043a\u0430\u043a \u0432 \u043e\u0442\u0432\u0435\u0442\u0435 \u043d\u0443\u0436\u043d\u043e \u0437\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u0431\u043e\u043b\u044c\u0448\u0438\u0439 \u0438\u0437 \u043a\u043e\u0440\u043d\u0435\u0439, \u043e\u0442\u0432\u0435\u0442\u043e\u043c \u0431\u0443\u0434\u0435\u0442 \\(6\\).<br><br><strong>\u041e\u0442\u0432\u0435\u0442: <\/strong>\\(6\\)<\/p>\n\n\n\n<p>\u041f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0440\u0435\u0448\u0438\u0442\u044c \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0442\u0435\u043e\u0440\u0435\u043c\u044b \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0438\u0444\u0430\u0433\u043e\u0440\u043e\u0432\u044b \u0442\u0440\u043e\u0439\u043a\u0438 \u0438 \u043a\u0430\u043a \u0438\u0445 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c?<\/strong><br><br>\u041f\u0438\u0444\u0430\u0433\u043e\u0440\u043e\u0432\u044b \u0442\u0440\u043e\u0439\u043a\u0438 \u2014 \u0442\u0440\u043e\u0439\u043a\u0438 \u043d\u0430\u0442\u0443\u0440\u0430\u043b\u044c\u043d\u044b\u0445 \u0447\u0438\u0441\u0435\u043b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0442 \u0442\u0435\u043e\u0440\u0435\u043c\u0435 \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430. \u0412\u043e\u0442 \u0442\u0430\u0431\u043b\u0438\u0446\u0430, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043f\u043e\u043a\u0430\u0437\u0430\u043d\u044b \u043f\u0435\u0440\u0432\u044b\u0435 7 \u043f\u0438\u0444\u0430\u0433\u043e\u0440\u043e\u0432\u044b\u0445 \u0442\u0440\u043e\u0435\u043a:<br><br><img decoding=\"async\" src=\"https:\/\/lh7-us.googleusercontent.com\/_njn2NgvGuX_I4YZHxH2GCo0E_1CFaS14tICEcX4py-WYns3w2eD0w_cFkxU6K4mHYNE3FMm0cEF-759yDuYTk4PzI6IEdsgLXhOrirgD8V3Q27pGy20WavHp7vWK_E3ATl7X-opoQgV8LGmwJ6OrVQ\" style=\"width: 450px;\"><br><br>\u041f\u0438\u0444\u0430\u0433\u043e\u0440\u043e\u0432\u044b \u0442\u0440\u043e\u0439\u043a\u0438 \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043d\u0430 \u044d\u043a\u0437\u0430\u043c\u0435\u043d\u0435 \u0434\u043b\u044f \u0431\u044b\u0441\u0442\u0440\u043e\u0433\u043e \u043f\u043e\u0434\u0441\u0447\u0435\u0442\u0430, \u0435\u0441\u043b\u0438 \u0432\u0430\u043c \u043f\u043e\u043f\u0430\u043b\u0430\u0441\u044c \u0442\u0435\u043e\u0440\u0435\u043c\u0430 \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430. \u0427\u0430\u0449\u0435 \u0432\u0441\u0435\u0433\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044e\u0442\u0441\u044f \u043f\u0435\u0440\u0432\u044b\u0435 3 \u043f\u0438\u0444\u0430\u0433\u043e\u0440\u043e\u0432\u044b \u0442\u0440\u043e\u0439\u043a\u0438.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u0422\u0435\u043f\u0435\u0440\u044c \u0434\u0430\u0432\u0430\u0439\u0442\u0435 \u0440\u0435\u0448\u0438\u043c \u0435\u0449\u0435 \u043e\u0434\u043d\u043e \u0437\u0430\u0434\u0430\u043d\u0438\u0435.<\/p>\n\n\n\n<p class=\"has-background\" 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 \u211610.\u00a0<\/strong><br><br><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435. <\/strong><em>\u0417\u0430\u0432\u043e\u0434 \u0440\u0435\u0448\u0438\u043b \u0443\u043c\u0435\u043d\u044c\u0448\u0438\u0442\u044c \u0432\u044b\u043f\u0443\u0441\u043a \u043f\u0440\u043e\u0434\u0443\u043a\u0446\u0438\u0438 \u043d\u0430 20%. \u041d\u0430 \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u043e\u0432 \u043d\u0443\u0436\u043d\u043e \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u0442\u044c \u0432\u044b\u043f\u0443\u0441\u043a \u043f\u0440\u043e\u0434\u0443\u043a\u0446\u0438\u0438, \u0447\u0442\u043e\u0431\u044b \u0434\u043e\u0441\u0442\u0438\u0433\u043d\u0443\u0442\u044c \u043f\u0440\u0435\u0436\u043d\u0435\u0433\u043e \u0443\u0440\u043e\u0432\u043d\u044f? \u041e\u0442\u0432\u0435\u0442 \u0437\u0430\u043f\u0438\u0448\u0438\u0442\u0435 \u0431\u0435\u0437 \u0437\u043d\u0430\u043a\u0430 \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u0430.<\/em><br><br><strong>\u0420\u0435\u0448\u0435\u043d\u0438\u0435.<\/strong> \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0447\u0435\u0440\u0442\u0435\u0436:<\/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\/03\/4-2-1024x143.png\" alt=\"\" class=\"wp-image-35635\" width=\"512\" height=\"72\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/4-2-1024x143.png 1024w, \/library\/wp-content\/uploads\/2024\/03\/4-2-300x42.png 300w, \/library\/wp-content\/uploads\/2024\/03\/4-2-768x107.png 768w, \/library\/wp-content\/uploads\/2024\/03\/4-2-1536x214.png 1536w, \/library\/wp-content\/uploads\/2024\/03\/4-2.png 1866w\" sizes=\"auto, (max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-background\" style=\"background-color:#f0e5ff\">\u041e\u0442\u0440\u0435\u0437\u043e\u043a \\(AB\\) \u2014 \u043f\u0435\u0440\u0432\u043e\u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u0439 \u0432\u044b\u043f\u0443\u0441\u043a \u043f\u0440\u043e\u0434\u0443\u043a\u0446\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043c\u044b \u0440\u0430\u0437\u0434\u0435\u043b\u0438\u043b\u0438 \u043d\u0430 5 \u0440\u0430\u0432\u043d\u044b\u0445 \u0447\u0430\u0441\u0442\u0435\u0439. \u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u0441\u043e\u043a\u0440\u0430\u0442\u0438\u043b\u0438 \u0432\u044b\u043f\u0443\u0441\u043a \u043f\u0440\u043e\u0434\u0443\u043a\u0446\u0438\u0438 \u043d\u0430 20%, \u043e\u043d \u0441\u0442\u0430\u043b \u0440\u0430\u0432\u0435\u043d \u043e\u0442\u0440\u0435\u0437\u043a\u0443 \\(AC\\), \u0442\u043e \u0435\u0441\u0442\u044c \u043c\u044b \u0443\u0431\u0440\u0430\u043b\u0438 \u0447\u0430\u0441\u0442\u044c \\(CB\\), \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0438 \u0440\u0430\u0432\u043d\u0430 20%.\u00a0<br><br>\u0422\u0435\u043f\u0435\u0440\u044c, \u0447\u0442\u043e\u0431\u044b \u0432\u0435\u0440\u043d\u0443\u0442\u044c \u043f\u0435\u0440\u0432\u043e\u043d\u0430\u0447\u0430\u043b\u044c\u043d\u044b\u0439 \u0432\u044b\u043f\u0443\u0441\u043a \u043f\u0440\u043e\u0434\u0443\u043a\u0446\u0438\u0438, \u043d\u0443\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438, \u043a\u0430\u043a\u0443\u044e \u0447\u0430\u0441\u0442\u044c \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 CB \u043e\u0442 AC. \u041e\u0442\u0432\u0435\u0442 \u0432\u0438\u0434\u0435\u043d \u0438\u0437 \u0447\u0435\u0440\u0442\u0435\u0436\u0430 \u2014 \\(\\frac{1}{4}AC=CB\\). \u0421\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u0438\u043c\u0435\u0435\u043c:<br><br>\\(\\frac{1}{4}*100\\%=25\\%\\)<br><br>\u041f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f, \u043d\u0443\u0436\u043d\u043e \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u0442\u044c \u043d\u0430 25%. \u041e\u0442\u0432\u0435\u0442 \u0437\u0430\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u043c \u0431\u0435\u0437 \u0437\u043d\u0430\u043a\u0430 \u043f\u0440\u043e\u0446\u0435\u043d\u0442\u0430.<br><br><strong>\u041e\u0442\u0432\u0435\u0442: <\/strong>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\/03\/image-351-1024x922.png\" alt=\"\" class=\"wp-image-35636\" width=\"388\" height=\"350\" srcset=\"\/library\/wp-content\/uploads\/2024\/03\/image-351-1024x922.png 1024w, \/library\/wp-content\/uploads\/2024\/03\/image-351-300x270.png 300w, \/library\/wp-content\/uploads\/2024\/03\/image-351-768x692.png 768w, \/library\/wp-content\/uploads\/2024\/03\/image-351-1536x1383.png 1536w, \/library\/wp-content\/uploads\/2024\/03\/image-351.png 1600w\" sizes=\"auto, (max-width: 388px) 100vw, 388px\" \/><\/figure><\/div>\n\n\n\n<p>\u041f\u043e\u0447\u0442\u0438 \u0432\u0441\u0435 \u0442\u0435\u043a\u0441\u0442\u043e\u0432\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043c\u043e\u0436\u043d\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u0441 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435\u043c \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438. \u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u0442\u0435\u043a\u0441\u0442\u043e\u0432\u044b\u0445 \u0437\u0430\u0434\u0430\u0447 \u043c\u044b \u0440\u0430\u0437\u0431\u0438\u0440\u0430\u043b\u0438 \u0432 \u0441\u0442\u0430\u0442\u044c\u0435 \u00ab\u0422\u0435\u043a\u0441\u0442\u043e\u0432\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438\u00bb.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\"><strong>\u041a\u0430\u043a \u0440\u0430\u0437\u0440\u0435\u0437\u0430\u0442\u044c \u0442\u043e\u0440\u0442 \u043d\u0430 8 \u043a\u0443\u0441\u043a\u043e\u0432 \u0437\u0430 \u0442\u0440\u0438 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f?<\/strong><br>\u0421\u043b\u0435\u0434\u0438\u0442\u0435 \u0437\u0430 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f\u043c\u0438:<br><img decoding=\"async\" src=\"https:\/\/lh7-us.googleusercontent.com\/T2WRZzcAdvEro3KTymnNXMKONWZabkwlfA3EfOrRKkFwd2obsIt4J434WehTKSDnj2BgrMTjb4RV3JqNWcC689souPTjhIsDaGMORYS_mIg77fjtKnTPvSWUFzIwmEBsBfqk7TUM4ET3jFBT4ouG75U\" style=\"width: 350px;\"><br>\u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0440\u0430\u0437\u0440\u0435\u0437\u0430\u0435\u043c \u0442\u043e\u0440\u0442 \u043d\u0430 \u0434\u0432\u0435 \u0447\u0430\u0441\u0442\u0438. \u0423 \u043d\u0430\u0441 \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u043e\u0441\u044c \u0434\u0432\u0430 \u0431\u043e\u043b\u044c\u0448\u0438\u0445 \u043a\u0443\u0441\u043a\u0430.<br><img decoding=\"async\" src=\"https:\/\/lh7-us.googleusercontent.com\/4Ku2OAe7iBkIaTV0aEBvF9p_s1gRZ-nYZESCivZwq2Ask6qHdvQ0eixeIoeUw2JjVvBjfRnVBQuodgbxgqtdqqCZUHN24lqKjYf95ptp__D_anh_rhMju08_WDAt2yebwuJQpO0K95NQIetMZ-uVMm4\" style=\"width: 350px;\"><br>\u0422\u0435\u043f\u0435\u0440\u044c \u0435\u0449\u0435 \u0440\u0430\u0437 \u0440\u0430\u0437\u0440\u0435\u0437\u0430\u0435\u043c \u0442\u043e\u0440\u0442, \u0438 \u0443 \u043d\u0430\u0441 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f 4 \u0447\u0430\u0441\u0442\u0438.\u00a0<br><img decoding=\"async\" src=\"https:\/\/lh7-us.googleusercontent.com\/aQ_n7jfgN4wmAUJgVoppJRFmb-DhoSWC-gHDeSiKciN6TL_Vk0Izo6Adpndi3Ii_Z1RwG_Wo-CDrBi9cO4SBAzSvFahVTCnjslYVD4PdDOv6jVryI3JMzrzpcMn-gEAZQlaHbQmrcFxYQPf0ej1AFlw\" style=\"width: 350px;\"><br>\u0418 \u043f\u043e\u0441\u043b\u0435\u0434\u043d\u0435\u0435 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u0435: \u043c\u044b \u0440\u0430\u0437\u0440\u0435\u0437\u0430\u0435\u043c \u0442\u043e\u0440\u0442 \u043d\u0435 \u043f\u043e \u0432\u0435\u0440\u0442\u0438\u043a\u0430\u043b\u0438, \u0430 \u043f\u043e \u0433\u043e\u0440\u0438\u0437\u043e\u043d\u0442\u0430\u043b\u0438. \u0418 \u0443 \u043d\u0430\u0441 \u043f\u043e\u043b\u0443\u0447\u0438\u043b\u043e\u0441\u044c \u043a\u0430\u043a \u0440\u0430\u0437 8 \u043a\u0443\u0441\u043a\u043e\u0432.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0440\u0430\u0437\u043e\u0431\u0440\u0430\u043b\u0438, \u043a\u0430\u043a \u043c\u043e\u0436\u043d\u043e \u0440\u0435\u0448\u0430\u0442\u044c \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0430\u043b\u0433\u0435\u0431\u0440\u044b \u0438 \u043d\u0430\u043e\u0431\u043e\u0440\u043e\u0442. \u0412 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0440\u0430\u0437 \u043c\u044b \u0443\u0437\u043d\u0430\u0435\u043c, \u043a\u0430\u043a \u0440\u0435\u0448\u0430\u0442\u044c <a href=\"https:\/\/umschool.net\/library\/matematika\/vvedenie-v-zadachi-s-parametrom-reshenie-uravnenij-s-parametrom\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0430\u043c\u0438.<\/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><strong>\u0418\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f<\/strong> \u2014 \u044d\u0442\u043e \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f, \u0432 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u043d\u0435\u0438\u0437\u0432\u0435\u0441\u0442\u043d\u043e\u0435 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043f\u043e\u0434 \u0437\u043d\u0430\u043a\u043e\u043c \u043a\u043e\u0440\u043d\u044f.<\/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>\u041e\u0442 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u043c\u043e\u0436\u043d\u043e \u043f\u0435\u0440\u0435\u0439\u0442\u0438 \u043a \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043c\u0435\u0442\u043e\u0434\u0430 \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u0438 \u043c\u0435\u0442\u043e\u0434\u0430 \u043e\u0431\u044a\u0435\u043c\u043e\u0432.<\/li><li>\u0412 \u0437\u0430\u0434\u0430\u0447\u0430\u0445 \u0441 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 \u0438\u0445 \u043d\u0435\u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0441\u0442\u0440\u043e\u0438\u0442\u044c \u2014 \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u043e\u0440\u043c\u0443\u043b\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0441\u0438\u043b\u044c\u043d\u043e \u0443\u0441\u043a\u043e\u0440\u044f\u044e\u0442 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u0440\u0435\u0448\u0435\u043d\u0438\u044f.<\/li><li>\u0414\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0438\u0440\u0440\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u044c\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0442\u0435\u043e\u0440\u0435\u043c\u0443 \u041f\u0438\u0444\u0430\u0433\u043e\u0440\u0430.<\/li><li>\u0418 \u0442\u0435\u043a\u0441\u0442\u043e\u0432\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0438\u0437 \u0415\u0413\u042d \u043f\u043e \u043f\u0440\u043e\u0444\u0438\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u043c\u043e\u0436\u043d\u043e \u0442\u043e\u0436\u0435 \u0440\u0435\u0448\u0430\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438.<\/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>\u0414\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u0438 \u0440\u043e\u043c\u0431\u0430 \u043e\u0442\u043d\u043e\u0441\u044f\u0442\u0441\u044f \u043a\u0430\u043a 3:4. \u041f\u0435\u0440\u0438\u043c\u0435\u0442\u0440 \u0440\u043e\u043c\u0431\u0430 \u0440\u0430\u0432\u0435\u043d 100. \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0432\u044b\u0441\u043e\u0442\u0443 \u0440\u043e\u043c\u0431\u0430.<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(24\\)<\/li><li>\\(96\\)<\/li><li>\\(48\\)<\/li><li>\\(192\\)\u00a0<\/li><\/ol>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 2.<\/strong><br>\u041f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b \u043b\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \\(a=\\{2, 10, -4\\}, b=\\{6, -2, 18\\}\\)?<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\u0414\u0430.<\/li><li>\u041d\u0435\u0442.<\/li><\/ol>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 3.<\/strong><br>\u041a\u0430\u043a\u0430\u044f \u0438\u0437 \u044d\u0442\u0438\u0445 \u0442\u0440\u043e\u0435\u043a \u043d\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0438\u0444\u0430\u0433\u043e\u0440\u043e\u0432\u043e\u0439?\u00a0<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>3, 4, 5<\/li><li>6, 8, 10<\/li><li>8, 15, 17<\/li><li>5, 11, 12<\/li><\/ol>\n\n\n\n<p><strong>\u0417\u0430\u0434\u0430\u043d\u0438\u0435 4.<\/strong><br>\u0417\u0430\u0432\u043e\u0434 \u0440\u0435\u0448\u0438\u043b \u0443\u043c\u0435\u043d\u044c\u0448\u0438\u0442\u044c \u0432\u044b\u043f\u0443\u0441\u043a \u043f\u0440\u043e\u0434\u0443\u043a\u0446\u0438\u0438 \u043d\u0430 10%. \u041d\u0430 \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043d\u0443\u0436\u043d\u043e \u0443\u0432\u0435\u043b\u0438\u0447\u0438\u0442\u044c \u0432\u044b\u043f\u0443\u0441\u043a \u043f\u0440\u043e\u0434\u0443\u043a\u0446\u0438\u0438, \u0447\u0442\u043e\u0431\u044b \u0434\u043e\u0441\u0442\u0438\u0433\u043d\u0443\u0442\u044c \u043f\u0440\u0435\u0436\u043d\u0435\u0433\u043e \u0443\u0440\u043e\u0432\u043d\u044f? \u041e\u0442\u0432\u0435\u0442 \u0437\u0430\u043f\u0438\u0448\u0438\u0442\u0435 \u0432 \u0432\u0438\u0434\u0435 \u043e\u0431\u044b\u043a\u043d\u043e\u0432\u0435\u043d\u043d\u043e\u0439 \u0434\u0440\u043e\u0431\u0438.<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>\\(11.1\\%\\)<\/li><li>\\(\\frac{1}{10}\\)<\/li><li>\\(\\frac{1}{9}\\)<\/li><li>\\(10\\%\\)<\/li><\/ol>\n\n\n\n<p><strong>\u041e\u0442\u0432\u0435\u0442\u044b: 1. \u2014 <\/strong>1;<strong> 2. \u2014 <\/strong>2;<strong> 3. \u2014 <\/strong>4;<strong> 4. \u2014 <\/strong>3.<\/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 \u0427\u0442\u043e \u043f\u043e\u044f\u0432\u0438\u043b\u043e\u0441\u044c \u043f\u0435\u0440\u0432\u0435\u0435: \u0430\u043b\u0433\u0435\u0431\u0440\u0430 \u0438\u043b\u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f? \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0438\u0444\u0430\u0433\u043e\u0440\u043e\u0432\u044b \u0442\u0440\u043e\u0439\u043a\u0438 \u0438 \u043a\u0430\u043a \u0438\u0445 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c? \u041a\u0430\u043a \u0440\u0430\u0437\u0440\u0435\u0437\u0430\u0442\u044c \u0442\u043e\u0440\u0442 \u043d\u0430 8 \u043a\u0443\u0441\u043a\u043e\u0432 \u0437\u0430 \u0442\u0440\u0438 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f? \u0412 \u044d\u0442\u043e\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0441 \u0432\u0430\u043c\u0438 \u0443\u0437\u043d\u0430\u0435\u043c \u043f\u0430\u0440\u043e\u0447\u043a\u0443 \u043b\u0430\u0439\u0444\u0445\u0430\u043a\u043e\u0432, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u043e\u043c\u043e\u0433\u0443\u0442 \u0440\u0435\u0448\u0430\u0442\u044c \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0430\u043b\u0433\u0435\u0431\u0440\u044b, \u0430 \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u2014 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0438. \u041f\u0440\u0438\u0441\u0442\u0443\u043f\u0438\u043c! \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":35623,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[1330,27],"class_list":["post-35622","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-geometricheskie-zadachi-s-elementami-algebry-i-naoborot","tag-matematika"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u044b \u0438 \u043d\u0430\u043e\u0431\u043e\u0440\u043e\u0442 - \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\/geometricheskie-zadachi-s-elementami-algebry-i-naoborot\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u0441 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c\u0438 \u0430\u043b\u0433\u0435\u0431\u0440\u044b \u0438 \u043d\u0430\u043e\u0431\u043e\u0440\u043e\u0442 - \u0423\u043c\u0441\u043a\u0443\u043b \u0423\u0447\u0435\u0431\u043d\u0438\u043a\" \/>\n<meta property=\"og:description\" content=\"\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435 \u0427\u0442\u043e \u043f\u043e\u044f\u0432\u0438\u043b\u043e\u0441\u044c \u043f\u0435\u0440\u0432\u0435\u0435: \u0430\u043b\u0433\u0435\u0431\u0440\u0430 \u0438\u043b\u0438 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u044f? \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043f\u0438\u0444\u0430\u0433\u043e\u0440\u043e\u0432\u044b \u0442\u0440\u043e\u0439\u043a\u0438 \u0438 \u043a\u0430\u043a \u0438\u0445 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c? \u041a\u0430\u043a \u0440\u0430\u0437\u0440\u0435\u0437\u0430\u0442\u044c \u0442\u043e\u0440\u0442 \u043d\u0430 8 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