{"id":2161,"date":"2022-04-01T15:05:48","date_gmt":"2022-04-01T15:05:48","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\/"},"modified":"2022-04-02T12:49:12","modified_gmt":"2022-04-02T12:49:12","slug":"substituce-kdy-a-jak-ji-v-rovnici-pouzit","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\/","title":{"rendered":"Substituce: kdy a jak ji v rovnici pou\u017e\u00edt"},"content":{"rendered":"<ul>\n<li>Substituce spo\u010d\u00edv\u00e1 v tom, \u017ee <strong>slo\u017eit\u00fd v\u00fdraz v rovnici<\/strong> nahrad\u00edme v\u00fdrazem jednodu\u0161\u0161\u00edm. T\u00edm vytvo\u0159\u00edme rovnici novou, kterou snadno vypo\u010d\u00edt\u00e1me. N\u00e1sledn\u011b se vr\u00e1t\u00edme na za\u010d\u00e1tek k v\u00fdrazu, kter\u00fd jsme substituovali a dopo\u010d\u00edt\u00e1me<\/li>\n<li>Pro substitu\u010dn\u00ed metodu <strong>neexistuje univerz\u00e1ln\u00ed pravidlo<\/strong>, kter\u00e9 by stanovovalo<strong> kdy a na jak\u00fd \u010dlen substituci pou\u017e\u00edt<\/strong><\/li>\n<li>Substitu\u010dn\u00ed metodu vyu\u017eijeme p\u0159i \u0159e\u0161en\u00ed rovnic, ve kter\u00fdch se v\u00fdraz (nebo jeho modifikace) vyskytuje v\u00edckr\u00e1t, nap\u0159\u00edklad:<\/li>\n<\/ul>\n<p>$${x}^{4}- {6x}^{2}+8=0$$<\/p>\n<p style=\"text-align: center\">Proto\u017ee se v rovnici vyskytuje x na \u010dtvrtou a x na druhou, p\u0159i\u010dem\u017e plat\u00ed, \u017ee<em><strong> x\u00b2=(x\u00b2)\u00b2<\/strong><\/em>,<\/p>\n<p style=\"text-align: center\">m\u016f\u017eemek substituci zvolit pr\u00e1v\u011b <em><strong>x\u00b2<\/strong><\/em><\/p>\n<p>$${x}^{2}=a$$<\/p>\n<p style=\"text-align: center\"><strong>T\u00edm n\u00e1m vznikne kvadratick\u00e1 rovnice, kterou snadno vypo\u010d\u00edt\u00e1me.<\/strong><\/p>\n<p>$${a}^{2}-6a+8=0$$<\/p>\n<p style=\"text-align: center\">s pou\u017eit\u00edm Vietov\u00fdch vzorc\u016f <em><strong>((ax\u00b2+bx+c=0 (x1+x2=-b; x1\u00b7x2=c))<\/strong><\/em> ur\u010d\u00edme ko\u0159eny t\u00e9to rovnice<\/p>\n<p style=\"text-align: center\"><strong><em>a1+a2=-b ; a1\u2022 a2=c<\/em><\/strong><\/p>\n<p style=\"text-align: center\"><strong><em>a1+a2=6\u00a0<\/em><\/strong><\/p>\n<p style=\"text-align: center\"><strong><em>a1\u2022a2=8<\/em><\/strong><\/p>\n<p style=\"text-align: center\">dostaneme tedy:<\/p>\n<p style=\"text-align: center\"><em><strong>a1=2; a2=4<\/strong><\/em><\/p>\n<p style=\"text-align: center\">V tuto chv\u00edli se mus\u00edme vr\u00e1tit na za\u010d\u00e1tek a dosad\u00edme oba ko\u0159eny do vztahu se substituc\u00ed<\/p>\n<p>$${x}^{2}=a$$<\/p>\n<p>$${x}^{2}=2\/\u221a$$<\/p>\n<p>$$x=\u00b1\\sqrt{2}$$<\/p>\n<p>$${x}^{2}=4\/\u221a$$<\/p>\n<p>$$x=\u00b12$$<\/p>\n<p style=\"text-align: center\"><strong><em>K={\u00b1\u221a2; \u00b12}<\/em><\/strong><\/p>\n","protected":false},"comment_status":"closed","ping_status":"closed","template":"","class_list":["post-2161","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>Substituce: kdy a jak ji v rovnici pou\u017e\u00edt | 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\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Substituce: kdy a jak ji v rovnici pou\u017e\u00edt | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Substituce spo\u010d\u00edv\u00e1 v tom, \u017ee slo\u017eit\u00fd v\u00fdraz v rovnici nahrad\u00edme v\u00fdrazem jednodu\u0161\u0161\u00edm. T\u00edm vytvo\u0159\u00edme rovnici novou, kterou snadno vypo\u010d\u00edt\u00e1me. N\u00e1sledn\u011b se vr\u00e1t\u00edme na za\u010d\u00e1tek k v\u00fdrazu, kter\u00fd jsme substituovali a dopo\u010d\u00edt\u00e1me Pro substitu\u010dn\u00ed metodu neexistuje univerz\u00e1ln\u00ed pravidlo, kter\u00e9 by stanovovalo kdy a na jak\u00fd \u010dlen substituci pou\u017e\u00edt Substitu\u010dn\u00ed metodu vyu\u017eijeme p\u0159i \u0159e\u0161en\u00ed rovnic, ve kter\u00fdch ... Read more\" \/>\n<meta property=\"og:url\" content=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\/\" \/>\n<meta property=\"og:site_name\" content=\"Studijni-svet.cz\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/studijnisvet\/\" \/>\n<meta property=\"article:modified_time\" content=\"2022-04-02T12:49:12+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Odhadovan\u00e1 doba \u010dten\u00ed\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minuta\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\\\/\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\\\/\",\"name\":\"Substituce: kdy a jak ji v rovnici pou\u017e\u00edt | Studijni-svet.cz\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#website\"},\"datePublished\":\"2022-04-01T15:05:48+00:00\",\"dateModified\":\"2022-04-02T12:49:12+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\\\/#breadcrumb\"},\"inLanguage\":\"cs\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/courses\\\/matematika-k-maturite\\\/lekce\\\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\u016f\",\"item\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Lekce\",\"item\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/lesson\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Matematika k maturit\u011b\",\"item\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/prehled\\\/matematika-k-maturite\\\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Substituce: kdy a jak ji v rovnici pou\u017e\u00edt\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#website\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/\",\"name\":\"Akademie Studijni-svet.cz | Kurzy a podklady\",\"description\":\"Online akademie | Kurzy a podklady\",\"publisher\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#organization\"},\"alternateName\":\"Akademie Studijni-svet.cz\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"cs\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#organization\",\"name\":\"Studijni-svet.cz\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"cs\",\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/wp-content\\\/uploads\\\/2022\\\/01\\\/SS_logo-1.png\",\"contentUrl\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/wp-content\\\/uploads\\\/2022\\\/01\\\/SS_logo-1.png\",\"width\":66,\"height\":75,\"caption\":\"Studijni-svet.cz\"},\"image\":{\"@id\":\"https:\\\/\\\/studijni-svet.cz\\\/kurzy\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/studijnisvet\\\/\",\"https:\\\/\\\/www.instagram.com\\\/studijnisvet.cz\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Substituce: kdy a jak ji v rovnici pou\u017e\u00edt | Studijni-svet.cz","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\/","og_locale":"cs_CZ","og_type":"article","og_title":"Substituce: kdy a jak ji v rovnici pou\u017e\u00edt | Studijni-svet.cz","og_description":"Substituce spo\u010d\u00edv\u00e1 v tom, \u017ee slo\u017eit\u00fd v\u00fdraz v rovnici nahrad\u00edme v\u00fdrazem jednodu\u0161\u0161\u00edm. T\u00edm vytvo\u0159\u00edme rovnici novou, kterou snadno vypo\u010d\u00edt\u00e1me. N\u00e1sledn\u011b se vr\u00e1t\u00edme na za\u010d\u00e1tek k v\u00fdrazu, kter\u00fd jsme substituovali a dopo\u010d\u00edt\u00e1me Pro substitu\u010dn\u00ed metodu neexistuje univerz\u00e1ln\u00ed pravidlo, kter\u00e9 by stanovovalo kdy a na jak\u00fd \u010dlen substituci pou\u017e\u00edt Substitu\u010dn\u00ed metodu vyu\u017eijeme p\u0159i \u0159e\u0161en\u00ed rovnic, ve kter\u00fdch ... Read more","og_url":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\/","og_site_name":"Studijni-svet.cz","article_publisher":"https:\/\/www.facebook.com\/studijnisvet\/","article_modified_time":"2022-04-02T12:49:12+00:00","twitter_card":"summary_large_image","twitter_misc":{"Odhadovan\u00e1 doba \u010dten\u00ed":"1 minuta"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\/","url":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\/","name":"Substituce: kdy a jak ji v rovnici pou\u017e\u00edt | Studijni-svet.cz","isPartOf":{"@id":"https:\/\/studijni-svet.cz\/kurzy\/#website"},"datePublished":"2022-04-01T15:05:48+00:00","dateModified":"2022-04-02T12:49:12+00:00","breadcrumb":{"@id":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\/#breadcrumb"},"inLanguage":"cs","potentialAction":[{"@type":"ReadAction","target":["https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/substituce-kdy-a-jak-ji-v-rovnici-pouzit\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Dom\u016f","item":"https:\/\/studijni-svet.cz\/kurzy\/"},{"@type":"ListItem","position":2,"name":"Lekce","item":"https:\/\/studijni-svet.cz\/kurzy\/lesson\/"},{"@type":"ListItem","position":3,"name":"Matematika k maturit\u011b","item":"https:\/\/studijni-svet.cz\/kurzy\/prehled\/matematika-k-maturite\/"},{"@type":"ListItem","position":4,"name":"Substituce: kdy a jak ji v rovnici pou\u017e\u00edt"}]},{"@type":"WebSite","@id":"https:\/\/studijni-svet.cz\/kurzy\/#website","url":"https:\/\/studijni-svet.cz\/kurzy\/","name":"Akademie Studijni-svet.cz | Kurzy a podklady","description":"Online akademie | Kurzy a podklady","publisher":{"@id":"https:\/\/studijni-svet.cz\/kurzy\/#organization"},"alternateName":"Akademie Studijni-svet.cz","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/studijni-svet.cz\/kurzy\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"cs"},{"@type":"Organization","@id":"https:\/\/studijni-svet.cz\/kurzy\/#organization","name":"Studijni-svet.cz","url":"https:\/\/studijni-svet.cz\/kurzy\/","logo":{"@type":"ImageObject","inLanguage":"cs","@id":"https:\/\/studijni-svet.cz\/kurzy\/#\/schema\/logo\/image\/","url":"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/01\/SS_logo-1.png","contentUrl":"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/01\/SS_logo-1.png","width":66,"height":75,"caption":"Studijni-svet.cz"},"image":{"@id":"https:\/\/studijni-svet.cz\/kurzy\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/studijnisvet\/","https:\/\/www.instagram.com\/studijnisvet.cz"]}]}},"_links":{"self":[{"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/lesson\/2161","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/lesson"}],"about":[{"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/types\/lesson"}],"replies":[{"embeddable":true,"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/comments?post=2161"}],"version-history":[{"count":0,"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/lesson\/2161\/revisions"}],"wp:attachment":[{"href":"https:\/\/studijni-svet.cz\/kurzy\/wp-json\/wp\/v2\/media?parent=2161"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}