{"id":2173,"date":"2022-04-01T17:25:57","date_gmt":"2022-04-01T17:25:57","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseny-priklad-1-3\/"},"modified":"2022-04-02T12:50:31","modified_gmt":"2022-04-02T12:50:31","slug":"reseny-priklad-1-3","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseny-priklad-1-3\/","title":{"rendered":"\u0158e\u0161en\u00fd p\u0159\u00edklad 1"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong> \u0158e\u0161te s pomoc\u00ed substituce rovnici (v mno\u017ein\u011b R).<\/p>\n<p>$${({x}^{2}-x+2)}^{2}-6({x}^{2}-x)-4=0$$<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>$${({x}^{2}-x+2)}^{2}-6({x}^{2}-x)-4=0$$<\/p>\n<p style=\"text-align: center\">v obou z\u00e1vork\u00e1ch se vyskytuje \u010dlen <strong><em>x\u00b2-x<\/em><\/strong>, budeme tedy substituovat ten<\/p>\n<p>$${x}^{2}-x=a$$<\/p>\n<p>$${(a+2)}^{2}-6a-4=0$$<\/p>\n<p>$${a}^{2}+4a+4-6a-4=0$$<\/p>\n<p>$${a}^{2}-2a=0$$<\/p>\n<p style=\"text-align: center\">S pou\u017eit\u00edm Vietov\u00fdch vzorc\u016f najdeme ko\u0159eny rovnice<\/p>\n<p style=\"text-align: center\"><em><strong>ax\u00b2+bx+c=0 (x1+x2=-b; x1\u00b7x2=c)<\/strong><\/em><\/p>\n<p style=\"text-align: center\"><em><strong>a1+a2=-b ; a1\u2022 a2=c<\/strong><\/em><\/p>\n<p style=\"text-align: center\"><em><strong>a1+a2=2<\/strong><\/em><\/p>\n<p style=\"text-align: center\"><em><strong>a1\u2022a2=0<\/strong><\/em><\/p>\n<p style=\"text-align: center\"><em><strong>a1=2; a2=0<\/strong><\/em><\/p>\n<p style=\"text-align: center\">Nyn\u00ed se m\u016f\u017eeme vr\u00e1tit ke vztahu:<\/p>\n<p>$${x}^{2}-x=a$$<\/p>\n<p style=\"text-align: center\">a naj\u00edt \u0159e\u0161en\u00ed pro <strong><em>0<\/em><\/strong> a <em><strong>2<\/strong><\/em><\/p>\n<p>$${x}^{2}-x=0$$<\/p>\n<p style=\"text-align: center\">Op\u011bt vyu\u017eijeme Vietov\u00fdch vzorc\u016f a najdeme oba ko\u0159eny<\/p>\n<p style=\"text-align: center\"><strong><em>x1+x2=1<\/em><\/strong><\/p>\n<p style=\"text-align: center\"><strong><em>x1\u2022x2=0<\/em><\/strong><\/p>\n<p style=\"text-align: center\"><strong><em>x1=0; x2=1<\/em><\/strong><\/p>\n<p>$${x}^{2}-x=2$$<\/p>\n<p>$${x}^{2}-x-2=0$$<\/p>\n<p style=\"text-align: center\">Op\u011bt vyu\u017eijeme Vietov\u00fdch vzorc\u016f a najdeme oba ko\u0159eny<\/p>\n<p style=\"text-align: center\"><strong><em>x1+x2=1<\/em><\/strong><\/p>\n<p style=\"text-align: center\"><strong><em>x1\u2022x2=-2<\/em><\/strong><\/p>\n<p style=\"text-align: center\"><strong><em>x1=-1; x2=2<\/em><\/strong><\/p>\n<p style=\"text-align: center\">\u0158e\u0161en\u00edm je:<\/p>\n<p style=\"text-align: center\"><strong><em>K={0;\u00b11;2}<\/em><\/strong><\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2173","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0158e\u0161en\u00fd p\u0159\u00edklad 1 | Studijni-svet.cz<\/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:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseny-priklad-1-3\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0158e\u0161en\u00fd p\u0159\u00edklad 1 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: \u0158e\u0161te s pomoc\u00ed substituce rovnici (v mno\u017ein\u011b R). $${({x}^{2}-x+2)}^{2}-6({x}^{2}-x)-4=0$$ \u0158e\u0161en\u00ed: $${({x}^{2}-x+2)}^{2}-6({x}^{2}-x)-4=0$$ v obou z\u00e1vork\u00e1ch se vyskytuje \u010dlen x\u00b2-x, budeme tedy substituovat ten $${x}^{2}-x=a$$ $${(a+2)}^{2}-6a-4=0$$ $${a}^{2}+4a+4-6a-4=0$$ $${a}^{2}-2a=0$$ S pou\u017eit\u00edm Vietov\u00fdch vzorc\u016f najdeme ko\u0159eny rovnice ax\u00b2+bx+c=0 (x1+x2=-b; x1\u00b7x2=c) a1+a2=-b ; a1\u2022 a2=c a1+a2=2 a1\u2022a2=0 a1=2; a2=0 Nyn\u00ed se m\u016f\u017eeme vr\u00e1tit ke vztahu: $${x}^{2}-x=a$$ a naj\u00edt \u0159e\u0161en\u00ed ... 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x1\u00b7x2=c) a1+a2=-b ; a1\u2022 a2=c a1+a2=2 a1\u2022a2=0 a1=2; a2=0 Nyn\u00ed se m\u016f\u017eeme vr\u00e1tit ke vztahu: $${x}^{2}-x=a$$ a naj\u00edt \u0159e\u0161en\u00ed ... 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