{"id":2348,"date":"2023-02-12T15:11:25","date_gmt":"2023-02-12T14:11:25","guid":{"rendered":"http:\/\/matma.com.pl\/?p=2348"},"modified":"2023-02-19T15:33:37","modified_gmt":"2023-02-19T14:33:37","slug":"zadanie-18-0-1-zbior-podstawa","status":"publish","type":"post","link":"http:\/\/matma.com.pl\/?p=2348","title":{"rendered":"zadanie 18 (0-1) zbi\u00f3r podstawa"},"content":{"rendered":"<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\frac{\\left&amp;space;(&amp;space;3x^2-6x&amp;space;\\right&amp;space;)\\left&amp;space;(&amp;space;x^2-9&amp;space;\\right&amp;space;)}{\\left&amp;space;(x-2&amp;space;\\right&amp;space;)\\left&amp;space;(x-3&amp;space;\\right&amp;space;)^2}=0\" alt=\"\\frac{\\left ( 3x^2-6x \\right )\\left ( x^2-9 \\right )}{\\left (x-2 \\right )\\left (x-3 \\right )^2}=0\" align=\"absmiddle\" \/><\/p>\n<p>Zacznijmy od wyznaczenia dziedziny:<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;x-2&amp;space;\\right&amp;space;)\\left&amp;space;(&amp;space;x-3&amp;space;\\right&amp;space;)^2\\neq&amp;space;0\" alt=\"\\left ( x-2 \\right )\\left ( x-3 \\right )^2\\neq 0\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?x-2\\neq&amp;space;0\\;&amp;space;\\;&amp;space;\\;&amp;space;\\wedge\\;&amp;space;\\;&amp;space;\\;&amp;space;\\left&amp;space;(&amp;space;x-3&amp;space;\\right&amp;space;)^2\\neq&amp;space;0\" alt=\"x-2\\neq 0\\; \\; \\; \\wedge\\; \\; \\; \\left ( x-3 \\right )^2\\neq 0\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?x\\neq&amp;space;2\\;&amp;space;\\;&amp;space;\\;&amp;space;\\wedge&amp;space;\\;&amp;space;\\;&amp;space;\\;&amp;space;\\left&amp;space;(&amp;space;x-3&amp;space;\\right&amp;space;)\\neq&amp;space;0\" alt=\"x\\neq 2\\; \\; \\; \\wedge \\; \\; \\; \\left ( x-3 \\right )\\neq 0\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?x\\neq&amp;space;2\\;&amp;space;\\;&amp;space;\\;&amp;space;\\wedge&amp;space;\\;&amp;space;\\;&amp;space;\\;&amp;space;x\\neq&amp;space;3\" alt=\"x\\neq 2\\; \\; \\; \\wedge \\; \\; \\; x\\neq 3\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?D:\" alt=\"D:\" align=\"absmiddle\" \/> \u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?x\\in&amp;space;\\mathbb{R}\\setminus&amp;space;\\left&amp;space;\\{&amp;space;2,3&amp;space;\\right&amp;space;\\}\" alt=\"x\\in \\mathbb{R}\\setminus \\left \\{ 2,3 \\right \\}\" align=\"absmiddle\" \/><\/p>\n<p>Pozostaje nam teraz rozwi\u0105za\u0107 r\u00f3wnanie<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\frac{\\left&amp;space;(&amp;space;3x^2-6x&amp;space;\\right&amp;space;)\\left&amp;space;(&amp;space;x^2-9&amp;space;\\right&amp;space;)}{\\left&amp;space;(x-2&amp;space;\\right&amp;space;)\\left&amp;space;(x-3&amp;space;\\right&amp;space;)^2}=0\\;&amp;space;\\;&amp;space;\\;&amp;space;\\Rightarrow&amp;space;\\;&amp;space;\\;&amp;space;\\;&amp;space;\\left&amp;space;(&amp;space;3x^2-6&amp;space;\\right&amp;space;)\\left&amp;space;(&amp;space;x^2-9&amp;space;\\right&amp;space;)=0\" alt=\"\\frac{\\left ( 3x^2-6x \\right )\\left ( x^2-9 \\right )}{\\left (x-2 \\right )\\left (x-3 \\right )^2}=0\\; \\; \\; \\Rightarrow \\; \\; \\; \\left ( 3x^2-6 \\right )\\left ( x^2-9 \\right )=0\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" class=\"alignleft\" src=\"http:\/\/latex.codecogs.com\/gif.latex?3x\\left&amp;space;(&amp;space;x-2\\right&amp;space;)\\left&amp;space;(&amp;space;x-3&amp;space;\\right&amp;space;)\\left&amp;space;(&amp;space;x+3&amp;space;\\right&amp;space;)=0\" alt=\"3x\\left ( x-2\\right )\\left ( x-3 \\right )\\left ( x+3 \\right )=0\" align=\"absmiddle\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?3x=0\\;&amp;space;\/:3\\;&amp;space;\\;&amp;space;\\;&amp;space;\\vee&amp;space;\\;&amp;space;\\;&amp;space;\\;&amp;space;x-2=0\\;&amp;space;\\;&amp;space;\\;&amp;space;\\vee&amp;space;\\;&amp;space;\\;&amp;space;\\;&amp;space;x-3=0\\;&amp;space;\\;&amp;space;\\;&amp;space;\\vee&amp;space;\\;&amp;space;\\;&amp;space;\\;&amp;space;x+3=0\" alt=\"3x=0\\; \/:3\\; \\; \\; \\vee \\; \\; \\; x-2=0\\; \\; \\; \\vee \\; \\; \\; x-3=0\\; \\; \\; \\vee \\; \\; \\; x+3=0\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?x=0\\;&amp;space;\\;&amp;space;\\;&amp;space;\\vee&amp;space;\\;&amp;space;\\;&amp;space;\\;&amp;space;x=2\\;\\notin&amp;space;D&amp;space;\\;&amp;space;\\;&amp;space;\\vee&amp;space;\\;&amp;space;\\;&amp;space;\\;&amp;space;x=3\\;\\notin&amp;space;D&amp;space;\\;&amp;space;\\;&amp;space;\\vee&amp;space;\\;&amp;space;\\;&amp;space;\\;&amp;space;x=-3\" alt=\"x=0\\; \\; \\; \\vee \\; \\; \\; x=2\\;\\notin D \\; \\; \\vee \\; \\; \\; x=3\\;\\notin D \\; \\; \\vee \\; \\; \\; x=-3\" align=\"absmiddle\" \/><\/p>\n<p>Rozwi\u0105zaniami naszego r\u00f3wnania s\u0105: <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?x=2\" alt=\"x=2\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?x=3\" alt=\"x=3\" align=\"absmiddle\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Zacznijmy od wyznaczenia dziedziny: \u00a0 Pozostaje nam teraz rozwi\u0105za\u0107 r\u00f3wnanie &nbsp; Rozwi\u0105zaniami naszego r\u00f3wnania s\u0105: ,<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[44],"tags":[],"class_list":["post-2348","post","type-post","status-publish","format-standard","hentry","category-matura"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>zadanie 18 (0-1) zbi\u00f3r podstawa - Matma.com.pl<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/matma.com.pl\/?p=2348\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"zadanie 18 (0-1) zbi\u00f3r podstawa - Matma.com.pl\" \/>\n<meta property=\"og:description\" content=\"Zacznijmy od wyznaczenia dziedziny: \u00a0 Pozostaje nam teraz rozwi\u0105za\u0107 r\u00f3wnanie &nbsp; 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