{"id":1468,"date":"2022-03-14T11:39:59","date_gmt":"2022-03-14T11:39:59","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseny-priklad-1\/"},"modified":"2022-03-23T09:35:20","modified_gmt":"2022-03-23T09:35:20","slug":"reseny-priklad-1","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/reseny-priklad-1\/","title":{"rendered":"\u0158e\u0161en\u00fd p\u0159\u00edklad"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong><\/p>\n<p>V oboru R \u0159e\u0161te:<\/p>\n<p>$$\\frac{{x}^{2}-5x}{x}\u22640$$<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>$$\\frac{{x}^{2}-5x}{x}\u22640$$<\/p>\n<p>Ne\u017e se pust\u00edme do \u0159e\u0161en\u00ed, ur\u010d\u00edme si podm\u00ednku, \u017ee <em><strong>x<\/strong><\/em> mus\u00ed b\u00fdt z mno\u017einy <em><strong>R<\/strong><\/em>, ale nesm\u00ed se rovnat nule, to zap\u00ed\u0161eme n\u00e1sledovn\u011b:<\/p>\n<p style=\"text-align: center\"><em><strong>x\u2208R<span id=\"MathJax-Element-7-Frame\" class=\"MathJax\" style=\"line-height: normal;font-size: 14px;text-indent: 0px;text-align: left;text-transform: none;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;padding: 0px;margin: 0px;color: #333333;font-family: Arial, sans-serif;background-color: #ffffff\" role=\"presentation\" data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mi mathvariant=&quot;normal&quot;&gt;$&lt;\/mi&gt;&lt;\/math&gt;\"><span id=\"MathJax-Span-41\" class=\"math\"><\/span><\/span>\\{0}<\/strong><\/em><\/p>\n<p>Tuto podm\u00ednku stanovujeme proto, proto\u017ee<em><strong> x<\/strong><\/em> se nach\u00e1z\u00ed ve jmenovateli. Jakmile by bylo <em><strong>x<\/strong> <\/em>rovno nule, zlomek by nem\u011bl smysl.<\/p>\n<p>Jakmile m\u00e1me podm\u00ednku stanovenou, m\u016f\u017eeme se pustit do \u0159e\u0161en\u00ed.<\/p>\n<p>Za\u010dneme t\u00edm, \u017ee si uprav\u00edme \u010ditatel:<\/p>\n<p>$$\\frac{{x}^{2}-5x}{x}\u22640$$<\/p>\n<p>$$\\frac{{x}\\dot{(x-5)}}{x}\u22640$$<\/p>\n<p>Proto\u017ee jmenovatel jsme ji\u017e vy\u0159e\u0161ili stanoven\u00edm podm\u00ednky a pro <em><strong>x<\/strong><\/em> nach\u00e1zej\u00edc\u00ed se v \u010ditateli p\u0159ed z\u00e1vorkou se vztahuje stejn\u00e1 podm\u00ednka, m\u016f\u017eeme se v\u011bnovat z\u00e1vorce v \u010ditateli:<\/p>\n<p>$$x-5\u22640$$<\/p>\n<p>$$x\u22645$$<\/p>\n<p>T\u00edm jsme z\u00edskali \u0159e\u0161en\u00ed, kter\u00e9 nap\u00ed\u0161eme pomoc\u00ed interval\u016f. Proto\u017ee<strong> x\u22600<\/strong>, bude interval u nuly otev\u0159en\u00fd. U \u010d\u00edsla 5 bude otev\u0159en\u00fd, proto\u017ee <strong>x\u22645<\/strong>.<\/p>\n<p>$$K=(-\u221e;0)\u222a(0;5&gt;$$<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-1468","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 | 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\/\" \/>\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 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: V oboru R \u0159e\u0161te: $$frac{{x}^{2}-5x}{x}\u22640$$ \u0158e\u0161en\u00ed: $$frac{{x}^{2}-5x}{x}\u22640$$ Ne\u017e se pust\u00edme do \u0159e\u0161en\u00ed, ur\u010d\u00edme si podm\u00ednku, \u017ee x mus\u00ed b\u00fdt z mno\u017einy R, ale nesm\u00ed se rovnat nule, to zap\u00ed\u0161eme n\u00e1sledovn\u011b: x\u2208R{0} Tuto podm\u00ednku stanovujeme proto, proto\u017ee x se nach\u00e1z\u00ed ve jmenovateli. 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