{"id":4721,"date":"2022-09-01T13:58:21","date_gmt":"2022-09-01T11:58:21","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/mocniny-a-odmocniny-priklad-1\/"},"modified":"2022-09-01T13:58:21","modified_gmt":"2022-09-01T11:58:21","slug":"mocniny-a-odmocniny-priklad-1","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/mocniny-a-odmocniny-priklad-1\/","title":{"rendered":"Mocniny a odmocniny &#8211; p\u0159\u00edklad 1"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong> Rozhodn\u011bte, zda jsou n\u00e1sleduj\u00edc\u00ed tvrzen\u00ed pravdiv\u00e1, \u010di nikoliv pro v\u0161echna <em><strong>a &gt; b &gt; 0<\/strong><\/em>:<br \/>(a) $$ (ab-2a)^{2}=a^{2}(b-2)^{2}$$<br \/>(b) $$ \\sqrt{a^{2}-b^{2}}=a-b$$<br \/>&nbsp;(c) $$ \\frac{a^{50}}{a^{10}}=a^{5}$$<br \/>(d) $$ a\\cdot \\sqrt{a}=\\sqrt{a^{3}}$$<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p><em>a) Prvn\u00ed v\u00fdrok &#8211; ANO<\/em> <br \/>1) Pot\u0159ebujeme zjednodu\u0161it tuto z\u00e1vorku:<br \/>$$(ab-2a)^{2}$$<br \/>2) Mnoho\u010dlen rozlo\u017e\u00edme dle vzore\u010dku:<br \/>$$(a+b)^{2}=a^{2}+2ab+b^{2}$$<br \/>$$a^{2}-b^{2}-4a^{2}b+4a^{2}$$<br \/>3) Vytkneme a na druhou:<br \/>$$a^{2}(b^{2}-4b+4)$$<br \/>4) V z\u00e1vorce je rozepsan\u00fd vzorec, zap\u00ed\u0161eme jej ve slo\u017een\u00e9 form\u011b:<br \/>$$a^{2}(b-2)^{2}$$<br \/>5) Z n\u00e1sleduj\u00edc\u00edho tvaru m\u016f\u017eeme usoudit, \u017ee zde je v\u00fdrok pravdiv\u00fd:<br \/>$$a^{2}(2-b)^{2}$$<\/p>\n<p><em>b) Druh\u00fd v\u00fdrok &#8211; NE<\/em> <br \/>1) Pokud by byl v\u00fdrok pravdiv\u00fd, neplatila by rovnost zadan\u00e9 rovnice v\u00fd\u0161e<br \/>$$\\sqrt{a^{2}-b^{2}}\u2260a-b$$<\/p>\n<p><em>c) T\u0159et\u00ed v\u00fdrok &#8211; NE<\/em> <br \/>1) Jednozna\u010dn\u011b nepravdiv\u00fd v\u00fdrok<br \/>$$\\frac{a^{50}}{a^{10}}=a^{40}$$<\/p>\n<p><em>d) \u010ctvrt\u00fd v\u00fdrok &#8211; ANO<\/em> <br \/>1) Odmocn\u00edme a p\u0159ed z\u00e1vorkou:<br \/>$$\\sqrt{a^{2}\\cdot a}$$<br \/>2) V\u00fdsledek se n\u00e1m rovn\u00e1 zad\u00e1n\u00ed:<br \/>$$\\sqrt{a^{3}}$$<\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 5-6 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-4721","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Mocniny a odmocniny - 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\/mocniny-a-odmocniny-priklad-1\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mocniny a odmocniny - p\u0159\u00edklad 1 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Rozhodn\u011bte, zda jsou n\u00e1sleduj\u00edc\u00ed tvrzen\u00ed pravdiv\u00e1, \u010di nikoliv pro v\u0161echna a &gt; b &gt; 0:(a) $$ (ab-2a)^{2}=a^{2}(b-2)^{2}$$(b) $$ sqrt{a^{2}-b^{2}}=a-b$$&nbsp;(c) $$ frac{a^{50}}{a^{10}}=a^{5}$$(d) $$ acdot sqrt{a}=sqrt{a^{3}}$$ \u0158e\u0161en\u00ed: a) Prvn\u00ed v\u00fdrok &#8211; ANO 1) Pot\u0159ebujeme zjednodu\u0161it tuto z\u00e1vorku:$$(ab-2a)^{2}$$2) Mnoho\u010dlen rozlo\u017e\u00edme dle vzore\u010dku:$$(a+b)^{2}=a^{2}+2ab+b^{2}$$$$a^{2}-b^{2}-4a^{2}b+4a^{2}$$3) Vytkneme a na druhou:$$a^{2}(b^{2}-4b+4)$$4) V z\u00e1vorce je rozepsan\u00fd vzorec, zap\u00ed\u0161eme jej ve slo\u017een\u00e9 form\u011b:$$a^{2}(b-2)^{2}$$5) Z ... 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