{"id":4758,"date":"2022-09-02T13:45:42","date_gmt":"2022-09-02T11:45:42","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-priklad-1\/"},"modified":"2022-09-02T13:45:42","modified_gmt":"2022-09-02T11:45:42","slug":"rovnice-priklad-1","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-priklad-1\/","title":{"rendered":"Rovnice &#8211; p\u0159\u00edklad 1"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong> $$\\frac{2}{3}\\cdot \\frac{x-2}{4}\\cdot x = 1 -\\frac{x}{6}$$<br \/><strong>\u0158e\u0161te v oboru <em>R<\/em>.<\/strong><\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>1) Nejprve vy\u0159e\u0161\u00edme rozn\u00e1soben\u00ed na lev\u00e9 stran\u011b:<br \/>$$\\frac{2x(x-2)}{12} = 1 -\\frac{x}{6}$$<br \/>2) Na lev\u00e9 stran\u011b se zbav\u00edme 2 p\u0159ed z\u00e1vorkou, vykr\u00e1t\u00edme ji se jmenovatelem:<br \/>$$\\frac{x(x-2)}{6} = 1 -\\frac{x}{6}$$<br \/>3) Nyn\u00ed se zbav\u00edme zlomku, proto vyn\u00e1sob\u00edme 6. D\u00e1le se zbav\u00edme z\u00e1vorky na lev\u00e9 stran\u011b, t\u00edm, \u017ee ji rozn\u00e1sob\u00edme:<br \/>$$x^{2}-2x=6-x$$<br \/>4) Pravou stanu (6 &#8211; x) p\u0159evedeme na levou, t\u00edm se n\u00e1m 2x pon\u00ed\u017e\u00ed<br \/>$$x^{2}-x-6=0$$<br \/>5) P\u0159evedeme do tvaru, ze kter\u00e9ho je mo\u017en\u00e9 ur\u010dit x1 a x2 ???<br \/>$$(x-3)(x+2)=0$$<br \/>$$x_{1}=3; x_{2}=-2$$<\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 5 minut<\/p>\n<p>Jedn\u00e1 se o p\u0159\u00edklad z maturitn\u00edho testu.<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-4758","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>Rovnice - 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\/rovnice-priklad-1\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rovnice - p\u0159\u00edklad 1 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: $$frac{2}{3}cdot frac{x-2}{4}cdot x = 1 -frac{x}{6}$$\u0158e\u0161te v oboru R. \u0158e\u0161en\u00ed: 1) Nejprve vy\u0159e\u0161\u00edme rozn\u00e1soben\u00ed na lev\u00e9 stran\u011b:$$frac{2x(x-2)}{12} = 1 -frac{x}{6}$$2) Na lev\u00e9 stran\u011b se zbav\u00edme 2 p\u0159ed z\u00e1vorkou, vykr\u00e1t\u00edme ji se jmenovatelem:$$frac{x(x-2)}{6} = 1 -frac{x}{6}$$3) Nyn\u00ed se zbav\u00edme zlomku, proto vyn\u00e1sob\u00edme 6. D\u00e1le se zbav\u00edme z\u00e1vorky na lev\u00e9 stran\u011b, t\u00edm, \u017ee ji rozn\u00e1sob\u00edme:$$x^{2}-2x=6-x$$4) Pravou ... 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