{"id":2090,"date":"2022-03-30T13:30:45","date_gmt":"2022-03-30T13:30:45","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/jak-resit-iracionalni-rovnice-krok-za-krokem\/"},"modified":"2022-03-30T13:31:06","modified_gmt":"2022-03-30T13:31:06","slug":"jak-resit-iracionalni-rovnice-krok-za-krokem","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/jak-resit-iracionalni-rovnice-krok-za-krokem\/","title":{"rendered":"Jak \u0159e\u0161it iracion\u00e1ln\u00ed rovnice: krok za krokem"},"content":{"rendered":"<ul>\n<li><strong>Existuj\u00ed dva zp\u016fsoby \u0159e\u0161en\u00ed iracion\u00e1ln\u00edch rovnic:<\/strong><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><strong>PRVN\u00cd ZP\u016eSOB \u0158E\u0160EN\u00cd:<\/strong><\/p>\n<ul>\n<li>P\u0159ed \u0159e\u0161en\u00edm iracion\u00e1ln\u00ed rovnice si <strong>v\u017edy stanov\u00edm, za jak\u00fdch podm\u00ednek jsou ob\u011b strany rovnice nez\u00e1porn\u00e9<\/strong>. Stanov\u00edm si tedy <strong>defini\u010dn\u00ed obor \u0159e\u0161en\u00ed<\/strong>, ve kter\u00e9m je dan\u00e1 rovnice platn\u00e1 a pust\u00edm se do po\u010d\u00edt\u00e1n\u00ed. <strong>Nakonec porovn\u00e1m v\u00fdsledek s defini\u010dn\u00edm oborem<\/strong>. <strong>\u010c\u00edsla, kter\u00e1 do defini\u010dn\u00edho oboru \u0159e\u0161en\u00ed spadaj\u00ed jsou \u0159e\u0161en\u00edm.<\/strong> \u010c\u00edsla, kter\u00e1 do defini\u010dn\u00edho oboru nespadaj\u00ed, nejsou \u0159e\u0161en\u00edm. Poj\u010fme si tento postup uk\u00e1zat v praxi:<\/li>\n<\/ul>\n<p>$$\\sqrt{x}=3$$<\/p>\n<ul>\n<li>Nejprve si ur\u010d\u00edme, za jak\u00e9 podm\u00ednky bude lev\u00e1 strana rovnice nez\u00e1porn\u00e1. To nastane tehdy, <strong>pokud bude v\u00fdraz pod odmocniou nez\u00e1porn\u00fd<\/strong>, tedy, pokud bude v\u011bt\u0161\u00ed roven nule, tzn.<em><strong> x\u22650<\/strong><\/em>. Z toho vypl\u00fdv\u00e1, \u017ee defini\u010dn\u00ed obor je <strong><em>&lt;0;\u221e)<\/em><\/strong>. Nyn\u00ed se ji\u017e m\u016f\u017eeme vrhnout do po\u010d\u00edt\u00e1n\u00ed.<\/li>\n<\/ul>\n<p>$$\\sqrt{x}=3$$<\/p>\n<p style=\"text-align: center\">Nejprve celou rovici umocn\u00edme:<\/p>\n<p>$${(\\sqrt{x})}^{2}={3}^{2}$$<\/p>\n<p>$$x=9$$<\/p>\n<p style=\"text-align: center\"><strong><em>K={9}<\/em><\/strong><\/p>\n<p>Proto\u017ee<strong> \u010d\u00edslo 9 se nach\u00e1z\u00ed v defini\u010dn\u00edm oboru<\/strong>, kter\u00fd jsme si na za\u010d\u00e1tku stanovili,<strong> je 9 spr\u00e1vn\u00fdm \u0159e\u0161en\u00edm rovnice<\/strong> a nen\u00ed nutn\u00e9 prov\u00e1d\u011bt zkou\u0161ku.<\/p>\n<p><strong>DRUH\u00dd ZP\u016ePOS \u0158E\u0160EN\u00cd:<\/strong><\/p>\n<ul>\n<li><strong>Rovnou se pust\u00edm do \u0159e\u0161en\u00ed rovnice bez stanoven\u00ed defini\u010dn\u00edh oboru<\/strong>. Po v\u00fdpo\u010dtu <em><strong>x<\/strong><\/em> <strong>provedu zkou\u0161ku<\/strong> pro v\u0161echna \u0159e\u0161en\u00ed.<\/li>\n<li>Op\u011bt si poj\u010fme uv\u00e9st n\u00e1zorn\u00fd p\u0159\u00edklad:<\/li>\n<\/ul>\n<p>$$\\sqrt{x}=3$$<\/p>\n<p style=\"text-align: center\">Abychom se zbavili odmocniny, ob\u011b strany v\u00fdrazu umocn\u00edme<\/p>\n<p>$${(\\sqrt{x})}^{2}={3}^{2}$$<\/p>\n<p style=\"text-align: center\">A rovnou dostaneme v\u00fdsledek:<\/p>\n<p>$$x=9$$<\/p>\n<p style=\"text-align: center\">Ne\u017e ale prohl\u00e1s\u00edme, \u017ee \u010d\u00edslo \u00ed je spr\u00e1vn\u00fdm \u0159e\u0161en\u00edm rovnice, mus\u00edme prov\u00e9st zkou\u0161ku dosazen\u00edm:<\/p>\n<p>$$L(9)=\\sqrt{9}=3$$<\/p>\n<p>$$P(9)=3$$<\/p>\n<p>$$L(9)=P(9)$$<\/p>\n<p style=\"text-align: center\">Proto\u017ee se ob\u011b strany po dosazen\u00ed \u010d\u00edsla 9 na m\u00edsto <strong><em>x<\/em><\/strong> rovnaj\u00ed, m\u016f\u017eeme prohl\u00e1sit, \u017ee 9 je spr\u00e1vn\u00fdm \u0159e\u0161en\u00edm.<\/p>\n<p style=\"text-align: center\"><strong><em>K={9}<\/em><\/strong><\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2090","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>Jak \u0159e\u0161it iracion\u00e1ln\u00ed rovnice: krok za krokem | 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\/jak-resit-iracionalni-rovnice-krok-za-krokem\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak \u0159e\u0161it iracion\u00e1ln\u00ed rovnice: krok za krokem | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Existuj\u00ed dva zp\u016fsoby \u0159e\u0161en\u00ed iracion\u00e1ln\u00edch rovnic: &nbsp; PRVN\u00cd ZP\u016eSOB \u0158E\u0160EN\u00cd: P\u0159ed \u0159e\u0161en\u00edm iracion\u00e1ln\u00ed rovnice si v\u017edy stanov\u00edm, za jak\u00fdch podm\u00ednek jsou ob\u011b strany rovnice nez\u00e1porn\u00e9. 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