{"id":4759,"date":"2022-09-02T13:53:34","date_gmt":"2022-09-02T11:53:34","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-priklad-2\/"},"modified":"2022-09-02T13:56:55","modified_gmt":"2022-09-02T11:56:55","slug":"rovnice-priklad-2","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/rovnice-priklad-2\/","title":{"rendered":"Rovnice &#8211; p\u0159\u00edklad 2"},"content":{"rendered":"<p style=\"text-align: center\" data-mce-style=\"text-align: center;\"><strong>Zad\u00e1n\u00ed:<\/strong> Ov\u011b\u0159te, kter\u00e1 z t\u011bchto rovnic m\u00e1 v oboru <strong><em>R<\/em><\/strong> pr\u00e1v\u011b jedno \u0159e\u0161en\u00ed:<br \/>$$a) x^{2}+1=0$$<br \/>$$b) (x+1)^{2}=x^{2}+1$$<br \/>$$c) x^{2}-1=0$$<br \/>$$d) x^{2}=x$$<br \/>e) \u017d\u00e1dn\u00e1 z v\u00fd\u0161e uveden\u00fdch rovnic<\/p>\n<p><\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p><em>a)<\/em> <strong>Rovnice nem\u00e1 v oboru R pr\u00e1v\u011b jedno \u0159e\u0161en\u00ed.<\/strong> <br \/>1) Dosad\u00edme do vzore\u010dku pro diskriminant<br \/>$$D=b^{2}\u22124\\cdot a\\cdot c$$<br \/>$$D=0^{2}-4\\cdot 1\\cdot 1$$<br \/>2) Nyn\u00ed vypo\u010d\u00edt\u00e1me diskriminant<br \/>$$D=-4\u21d2\u00f8$$<br \/><em>&nbsp; b)<\/em> <strong>Rovnice m\u00e1 v oboru R pr\u00e1v\u011b jedno \u0159e\u0161en\u00ed.<\/strong> <br \/>1) Rozep\u00ed\u0161eme prvn\u00ed z\u00e1vorku podle vzore\u010dku<br \/>$$(a+b)^{2}=a^{2}+2ab+b^{2}$$<br \/>$$(x+1)^{2}=x^{2}+1$$<br \/>$$x^{2}+2x+1=x^{2}+1$$<br \/>2) Nezn\u00e1m\u00e9 si ponech\u00e1me na jedn\u00e9 stran\u011b a \u010d\u00edsla p\u0159evedeme na druhou<br \/>$$2x=0$$<br \/>3) Vypo\u010d\u00edt\u00e1me pro 1x, v\u00fdsledek se v tomto p\u0159\u00edpad\u011b nezm\u011bn\u00ed, rovnice m\u00e1 1 \u0159e\u0161en\u00ed<br \/>$$x=0$$<br \/>&nbsp;<em> c)<\/em> <strong>Rovnice nem\u00e1 v oboru R pr\u00e1v\u011b jedno \u0159e\u0161en\u00ed (m\u00e1 dv\u011b \u0159e\u0161en\u00ed).<\/strong> <br \/>1) Na lev\u00e9 stan\u011b m\u00e1me op\u011bt schovan\u00fd vzore\u010dek, d\u00e1me jej do slo\u017een\u00e9ho stavu:<br \/>$$x^{2}-1=0$$<br \/>$$(x-1)(x+1)=0$$<br \/>2) Existuj\u00ed dv\u011b \u0159e\u0161en\u00ed<br \/>$$x_{1}=1; x_{2}=-1$$<br \/>&nbsp; <em>d)<\/em> <strong>Rovnice nem\u00e1 v oboru R pr\u00e1v\u011b jedno \u0159e\u0161en\u00ed (m\u00e1 dv\u011b \u0159e\u0161en\u00ed).<\/strong> <br \/>1) Rovnici si uprav\u00edme, tak abychom mohli ov\u011b\u0159it platnost:<br \/>$$x^{2}=x$$<br \/>$$x^{2}-x=0$$<br \/>2)<br \/>$$x(x-1)=0$$<br \/>3) Existuj\u00ed dv\u011b \u0159e\u0161en\u00ed<br \/>$$x_{1}=0; x_{2}=1$$<\/p>\n<p><strong>Rovnice z p\u0159\u00edkladu b) m\u00e1 v oboru R pr\u00e1v\u011b jedno \u0159e\u0161en\u00ed.<\/strong><\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 7 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-4759","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 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\/rovnice-priklad-2\/\" \/>\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 2 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Ov\u011b\u0159te, kter\u00e1 z t\u011bchto rovnic m\u00e1 v oboru R pr\u00e1v\u011b jedno \u0159e\u0161en\u00ed:$$a) x^{2}+1=0$$$$b) (x+1)^{2}=x^{2}+1$$$$c) x^{2}-1=0$$$$d) x^{2}=x$$e) \u017d\u00e1dn\u00e1 z v\u00fd\u0161e uveden\u00fdch rovnic \u0158e\u0161en\u00ed: a) Rovnice nem\u00e1 v oboru R pr\u00e1v\u011b jedno \u0159e\u0161en\u00ed. 1) Dosad\u00edme do vzore\u010dku pro diskriminant$$D=b^{2}\u22124cdot acdot c$$$$D=0^{2}-4cdot 1cdot 1$$2) Nyn\u00ed vypo\u010d\u00edt\u00e1me diskriminant$$D=-4\u21d2\u00f8$$&nbsp; b) Rovnice m\u00e1 v oboru R pr\u00e1v\u011b jedno \u0159e\u0161en\u00ed. 1) ... 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