{"id":2038,"date":"2022-03-30T09:03:55","date_gmt":"2022-03-30T09:03:55","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseny-priklad-2-2\/"},"modified":"2022-04-01T17:42:05","modified_gmt":"2022-04-01T17:42:05","slug":"reseny-priklad-2-2","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseny-priklad-2-2\/","title":{"rendered":"\u0158e\u0161en\u00fd p\u0159\u00edklad 2"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong><\/p>\n<p>\u0158e\u0161te rovnici (v mno\u017ein\u011b R):<\/p>\n<p>$$\\frac{{x}^{2}-4}{{x}^{2}-x-6}-\\frac{3}{2}=0$$<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>Za\u010dneme t\u00edm, \u017ee si \u010ditatel uprav\u00edme podle vzorce <em><strong>a\u00b2-b\u00b2=(a+b)(a-b)<\/strong>,<\/em> jmenovatel podle <strong>Vietov\u00fdch vzorc\u016f <em>ax\u00b2+bx+c=0 (x1+x2=-b; x1\u00b7x2=c) <\/em><\/strong>a zlomek bez <em><strong>x<\/strong><\/em> p\u0159esuneme na pravou stranu. Dostaneme:<\/p>\n<p>$$\\frac{(x+2)(x-2)}{(x+2)(x-3)}=\\frac{3}{2}$$<\/p>\n<p>V tuto chv\u00edli si stanov\u00edme podm\u00ednky pro<strong><em> x<\/em><\/strong>, kter\u00e9 budou n\u00e1sleduj\u00edc\u00ed:<strong><em> x\u2260-2 <\/em><\/strong>a <strong><em>x\u22603<\/em><\/strong>, jinak by ve jmenovateli byla nula. Z\u00e1rove\u0148 m\u016f\u017eeme odstranit z\u00e1vorku obsahuj\u00edc\u00ed v\u00fdraz <em><strong>(x+2) <\/strong><\/em>a zlomek takzvan\u011b zkr\u00e1tit.<\/p>\n<p>$$\\frac{x-2}{x-3}=\\frac{3}{2}$$<\/p>\n<p>Nyn\u00ed celou rovnici vyn\u00e1sob\u00edme v\u00fdrazem <strong><em>2(x-3) <\/em><\/strong>a dostaneme:<\/p>\n<p>$$2(x-2)=3(x-3)$$<\/p>\n<p>$$2x-4=3x-9$$<\/p>\n<p>$$x=5$$<\/p>\n<p style=\"text-align: center\"><em><strong>K={5}<\/strong><\/em><\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2038","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u0158e\u0161en\u00fd p\u0159\u00edklad 2 | 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-2-2\/\" \/>\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 2 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: \u0158e\u0161te rovnici (v mno\u017ein\u011b R): $$frac{{x}^{2}-4}{{x}^{2}-x-6}-frac{3}{2}=0$$ \u0158e\u0161en\u00ed: Za\u010dneme t\u00edm, \u017ee si \u010ditatel uprav\u00edme podle vzorce a\u00b2-b\u00b2=(a+b)(a-b), jmenovatel podle Vietov\u00fdch vzorc\u016f ax\u00b2+bx+c=0 (x1+x2=-b; x1\u00b7x2=c) a zlomek bez x p\u0159esuneme na pravou stranu. Dostaneme: $$frac{(x+2)(x-2)}{(x+2)(x-3)}=frac{3}{2}$$ V tuto chv\u00edli si stanov\u00edme podm\u00ednky pro x, kter\u00e9 budou n\u00e1sleduj\u00edc\u00ed: x\u2260-2 a x\u22603, jinak by ve jmenovateli byla nula. Z\u00e1rove\u0148 ... 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Dostaneme: $$frac{(x+2)(x-2)}{(x+2)(x-3)}=frac{3}{2}$$ V tuto chv\u00edli si stanov\u00edme podm\u00ednky pro x, kter\u00e9 budou n\u00e1sleduj\u00edc\u00ed: x\u2260-2 a x\u22603, jinak by ve jmenovateli byla nula. Z\u00e1rove\u0148 ... 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