{"id":2640,"date":"2022-05-02T11:52:56","date_gmt":"2022-05-02T09:52:56","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/binomicka-veta-reseny-priklad\/"},"modified":"2022-05-02T18:29:27","modified_gmt":"2022-05-02T16:29:27","slug":"binomicka-veta-reseny-priklad","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/binomicka-veta-reseny-priklad\/","title":{"rendered":"Binomick\u00e1 v\u011bta &#8211; \u0159e\u0161en\u00fd p\u0159\u00edklad"},"content":{"rendered":"<p>Pro ov\u011b\u0159en\u00ed toho, \u017ee dok\u00e1\u017eete vyu\u017e\u00edt Pascal\u016fv troj\u00faheln\u00edk p\u0159i odvozen\u00ed binomick\u00e9ho rozvoje, si poj\u010fme spole\u010dn\u011b vy\u0159e\u0161it p\u0159\u00edklad.<\/p>\n<p><strong>Zad\u00e1n\u00ed:\u00a0<\/strong><\/p>\n<p>S pomoc\u00ed Pascalova troj\u00faheln\u00edku odvo\u010fte v\u00fdpo\u010det pro:<\/p>\n<p>$${(a+b)}^{5}$$<\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>K \u0159e\u0161en\u00ed si mus\u00edme sepsat Pascal\u016fv troj\u00faheln\u00edk, co\u017e nen\u00ed nic slo\u017eit\u00e9ho, kdy\u017e v\u00edme, \u017ee se jedn\u00e1 o troj\u00faheln\u00edk za\u010d\u00ednaj\u00edc\u00ed 1 a dal\u0161\u00ed \u010dleny jsou v\u017edy sou\u010dtem \u010dlen\u016f nad nimi. Pomoci n\u00e1m mohou tak\u00e9 kombina\u010dn\u00ed \u010d\u00edsla a jejich seps\u00e1n\u00ed pro <strong><em>n=5<\/em><\/strong>.<\/p>\n<p style=\"text-align: center\">\u0158e\u0161en\u00ed s pomoc\u00ed vyps\u00e1n\u00ed Pascalova troj\u00faheln\u00edku pomoc\u00ed \u010d\u00edslic:<\/p>\n<p>$$\\begin{matrix}<br \/>\n&amp;&amp;&amp;&amp;&amp;1\\\\<br \/>\n&amp;&amp;&amp;&amp;1&amp;&amp;1\\\\<br \/>\n&amp;&amp;&amp;1&amp;&amp;2&amp;&amp;1\\\\<br \/>\n&amp;&amp;1&amp;&amp;3&amp;&amp;3&amp;&amp;1\\\\<br \/>\n&amp;1&amp;&amp;4&amp;&amp;6&amp;&amp;4&amp;&amp;1\\\\<br \/>\n1&amp;&amp;5&amp;&amp;10&amp;&amp;10&amp;&amp;5&amp;&amp;1<br \/>\n\\end{matrix}$$<\/p>\n<p style=\"text-align: center\">Pod\u00edv\u00e1me se na \u0161est\u00fd \u0159\u00e1dek troj\u00faheln\u00edku (st\u00e1le m\u011bjme na pam\u011bti, \u017ee prvn\u00ed \u0159\u00e1dek je ur\u010den pro<em><strong> n=0<\/strong><\/em>, proto <strong><em>n=5<\/em> <\/strong>najdeme na \u0161est\u00e9m \u0159\u00e1dku) a op\u00ed\u0161eme si \u010d\u00edsla.<\/p>\n<p style=\"text-align: center\">\u0158e\u0161en\u00ed pomoc\u00ed vyps\u00e1n\u00ed \u0159\u00e1dku, ve kter\u00e9m je n=5 s pomoc\u00ed kombina\u010dn\u00edch \u010d\u00edsel:<\/p>\n<p>$$\\binom{5}{0}\\binom{5}{1}\\binom{5}{2}\\binom{5}{3}\\binom{5}{4}\\binom{5}{5}$$<\/p>\n<p style=\"text-align: center\"><strong>1, 5, 10, 10, 5,1<\/strong><\/p>\n<p style=\"text-align: center\">V\u00edme, \u017ee tato \u010d\u00edsla se budou vyskytovat ve vzorci, tak\u017ee je do n\u011bj dopln\u00edme:<\/p>\n<p>$${(a+b)}^{5}={a}^{5}+5{a}^{4}b+10{a}^{3}{b}^{2}+10{a}^{2}{b}^{3}+5a{b}^{4}+{b}^{5}$$<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2640","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>Binomick\u00e1 v\u011bta - \u0159e\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\/binomicka-veta-reseny-priklad\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Binomick\u00e1 v\u011bta - \u0159e\u0161en\u00fd p\u0159\u00edklad | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Pro ov\u011b\u0159en\u00ed toho, \u017ee dok\u00e1\u017eete vyu\u017e\u00edt Pascal\u016fv troj\u00faheln\u00edk p\u0159i odvozen\u00ed binomick\u00e9ho rozvoje, si poj\u010fme spole\u010dn\u011b vy\u0159e\u0161it p\u0159\u00edklad. Zad\u00e1n\u00ed:\u00a0 S pomoc\u00ed Pascalova troj\u00faheln\u00edku odvo\u010fte v\u00fdpo\u010det pro: $${(a+b)}^{5}$$ \u0158e\u0161en\u00ed: K \u0159e\u0161en\u00ed si mus\u00edme sepsat Pascal\u016fv troj\u00faheln\u00edk, co\u017e nen\u00ed nic slo\u017eit\u00e9ho, kdy\u017e v\u00edme, \u017ee se jedn\u00e1 o troj\u00faheln\u00edk za\u010d\u00ednaj\u00edc\u00ed 1 a dal\u0161\u00ed \u010dleny jsou v\u017edy sou\u010dtem \u010dlen\u016f nad ... 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Zad\u00e1n\u00ed:\u00a0 S pomoc\u00ed Pascalova troj\u00faheln\u00edku odvo\u010fte v\u00fdpo\u010det pro: $${(a+b)}^{5}$$ \u0158e\u0161en\u00ed: K \u0159e\u0161en\u00ed si mus\u00edme sepsat Pascal\u016fv troj\u00faheln\u00edk, co\u017e nen\u00ed nic slo\u017eit\u00e9ho, kdy\u017e v\u00edme, \u017ee se jedn\u00e1 o troj\u00faheln\u00edk za\u010d\u00ednaj\u00edc\u00ed 1 a dal\u0161\u00ed \u010dleny jsou v\u017edy sou\u010dtem \u010dlen\u016f nad ... 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