{"id":1488,"date":"2022-03-14T12:22:50","date_gmt":"2022-03-14T12:22:50","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/na-co-si-dat-pri-reseni-nerovnic-pozor\/"},"modified":"2022-03-14T21:38:27","modified_gmt":"2022-03-14T21:38:27","slug":"na-co-si-dat-pri-reseni-nerovnic-pozor","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/na-co-si-dat-pri-reseni-nerovnic-pozor\/","title":{"rendered":"Na co si d\u00e1t p\u0159\u00ed \u0159e\u0161en\u00ed nerovnic pozor"},"content":{"rendered":"<ul>\n<li>P\u0159esto\u017ee nerovnice toho maj\u00ed s rovnicemi mnoho spole\u010dn\u00e9ho, existuj\u00ed v\u011bci, na kter\u00e9 si p\u0159i \u0159e\u0161en\u00ed nerovnic mus\u00edme d\u00e1t pozor.<\/li>\n<li><strong>P\u0159i \u0159e\u0161en\u00ed nerovnic postupujeme stejn\u011b, jako kdy\u017e \u0159e\u0161\u00edme rovnice.<\/strong> V\u00fdrazy s nezn\u00e1mou p\u0159esouv\u00e1me na jednu stranu a zbytek na druhou.<\/li>\n<li>B\u011bhem \u00faprav ale nesm\u00edme danou nerovnost zm\u011bnit! Co to znamen\u00e1?<\/li>\n<li>Je-li p\u0159ed \u00fapravou lev\u00e1 strana men\u0161\u00ed ne\u017e prav\u00e1,<strong> mus\u00ed to tak z\u016fstat i po \u00faprav\u011b<\/strong>. To plat\u00ed i v p\u0159\u00edpad\u011b, \u017ee srtany nerovnice oto\u010d\u00edme.<\/li>\n<li>P\u0159\u00edklad: <em><strong>7&gt;3<\/strong><\/em> je to stejn\u00e9 jako <strong><em>3&lt;7\u00a0<\/em><\/strong>(obr\u00e1tili jsme strany nerovnice a sou\u010dasn\u011b tak\u00e9 oto\u010dili znam\u00e9nko nerovnosti, aby byla nerovnost zachov\u00e1na)<\/li>\n<li>Kdykoliv, <strong>kdy\u017e nerovnici n\u00e1sob\u00edte z\u00e1porn\u00fdm \u010d\u00edslem, mus\u00edte obr\u00e1tit znam\u00e9nko nerovnosti!<\/strong><\/li>\n<li>P\u0159\u00edklad: $$2 &lt; 4$$<\/li>\n<li>Ur\u010dit\u011b se shodneme, \u017ee toto tvrzen\u00ed je pravdiv\u00e9, tedy \u017ee nerovnost, kter\u00e1 tvrd\u00ed, \u017ee dvojka je men\u0161\u00ed ne\u0159 \u010dty\u0159ka, je pravdiv\u00e1. Co se ale stane, pokud celou nerovnici vyn\u00e1sob\u00edme \u010d\u00edslem minus jedna? Dostaneme n\u00e1sledu\u00edc\u00ed nerovnici:<\/li>\n<\/ul>\n<p>$$-2&lt;-4$$<\/p>\n<ul>\n<li>Na prvn\u00ed pohled je patrn\u00e9, \u017ee tato nerovnice nen\u00ed pravdiv\u00e1. N\u00e1soben\u00ed nerovnice z\u00e1porn\u00fdm \u010d\u00edslem toti\u017e nen\u00ed evkivalentn\u00ed \u00faprava. Proto plat\u00ed pravidlo, \u017ee kdykoliv vyn\u00e1sob\u00edte nerovnici ibovoln\u00fdm z\u00e1porn\u00fdm \u010d\u00edslem, mus\u00edte oto\u010dit znam\u00e9nko nerovnosti. Po \u00faprav\u011b tedy dostanete nerovnost:<\/li>\n<\/ul>\n<p>$$-2&gt;-4$$<\/p>\n<ul>\n<li>Zbyl\u00e9 operace:<strong> p\u0159i\u010d\u00edt\u00e1n\u00ed, od\u010d\u00edt\u00e1n\u00ed, d\u011blen\u00ed a n\u00e1soben\u00ed kladn\u00fdm v\u00fdrazem jsou ekvivalentn\u00ed a nemus\u00edte m\u011bnit znam\u00e9nka nerovnosti.<\/strong><\/li>\n<li>P\u0159\u00edklad:\u00a0 Nerovnici $$\\frac{1}{{x}^{2}}&gt;4$$<\/li>\n<\/ul>\n<p>m\u016f\u017eeme vyn\u00e1sobit v\u00fdrazem <em><strong>x\u00b2<\/strong><\/em>\u00a0a dostat tak nerovnici: $${1}&gt;{4x}^{2}$$<\/p>\n<p>Mus\u00edme ov\u0161em stanovit podm\u00ednku, \u017ee<strong><em> x\u22600<\/em><\/strong>, proto\u017ee se nach\u00e1z\u00ed ve jmenovateli a dob\u0159e v\u00edme, \u017ee jmenovatel se nesm\u00ed rovnat nule.<\/p>\n<ul>\n<li>Ov\u0161em pozor! Nach\u00e1z\u00ed-li se ve jmenovateli pouze <em><strong>x<\/strong><\/em>, nesm\u00edme nerovnici nezn\u00e1mou vyn\u00e1sobit. Pro\u010d? Nev\u00edme toti\u017e, zda je <strong><em>x<\/em><\/strong> men\u0161\u00ed \u010di v\u011bt\u0161\u00ed jak nula. Proto je postup \u0159e\u0161en\u00ed nerovnice s nezn\u00e1mou ve jmenovateli specifick\u00fd. P\u0159edchoz\u00ed nerovnici jsme mohli vyn\u00e1sobit v\u00fdrazem <em><strong>x\u00b2<\/strong><\/em> , proto\u017ee <em><strong>x\u00b2<\/strong><\/em> je v\u017edy nez\u00e1porn\u00fd v\u00fdraz!<\/li>\n<\/ul>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1488","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>Na co si d\u00e1t p\u0159\u00ed \u0159e\u0161en\u00ed nerovnic pozor | 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\/na-co-si-dat-pri-reseni-nerovnic-pozor\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Na co si d\u00e1t p\u0159\u00ed \u0159e\u0161en\u00ed nerovnic pozor | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"P\u0159esto\u017ee nerovnice toho maj\u00ed s rovnicemi mnoho spole\u010dn\u00e9ho, existuj\u00ed v\u011bci, na kter\u00e9 si p\u0159i \u0159e\u0161en\u00ed nerovnic mus\u00edme d\u00e1t pozor. P\u0159i \u0159e\u0161en\u00ed nerovnic postupujeme stejn\u011b, jako kdy\u017e \u0159e\u0161\u00edme rovnice. V\u00fdrazy s nezn\u00e1mou p\u0159esouv\u00e1me na jednu stranu a zbytek na druhou. B\u011bhem \u00faprav ale nesm\u00edme danou nerovnost zm\u011bnit! Co to znamen\u00e1? Je-li p\u0159ed \u00fapravou lev\u00e1 strana men\u0161\u00ed ... 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P\u0159i \u0159e\u0161en\u00ed nerovnic postupujeme stejn\u011b, jako kdy\u017e \u0159e\u0161\u00edme rovnice. V\u00fdrazy s nezn\u00e1mou p\u0159esouv\u00e1me na jednu stranu a zbytek na druhou. B\u011bhem \u00faprav ale nesm\u00edme danou nerovnost zm\u011bnit! Co to znamen\u00e1? Je-li p\u0159ed \u00fapravou lev\u00e1 strana men\u0161\u00ed ... 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