{"id":21223,"date":"2021-07-19T20:35:42","date_gmt":"2021-07-19T15:05:42","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=21223"},"modified":"2021-07-19T20:42:20","modified_gmt":"2021-07-19T15:12:20","slug":"02-01-00-q1","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/02-01-00-q1\/","title":{"rendered":"\u0d9c\u0dab\u0d9a \u0dba\u0db1\u0dca\u0dad\u0dca\u200d\u0dbb \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dcf \u0db1\u0ddc\u0d9a\u0dbb \u0db8\u0dd9\u0dc4\u0dd2 \u0d85\u0d9c\u0dba \u0dc4\u0ddc\u0dba\u0db1\u0dca\u0db1 \u0d94\u0dba\u0dcf\u0dbd\u0da7\u0dad\u0dca \u0db4\u0dd4\u0dc5\u0dd4\u0dc0\u0db1\u0dca\u0daf \u0db6\u0dbd\u0db1\u0dca\u0db1&#8230;"},"content":{"rendered":"\n<p class=\"has-text-align-center has-text-color has-background\" style=\"background-color:#e0c8f8;color:#000532;font-size:30px\"><strong><span class=\"wp-katex-eq\" data-display=\"false\">\\sqrt[3]{8+3\\sqrt{21}}\\;+\\;\\sqrt[3]{8-3\\sqrt{21}}<\/span><\/strong><\/p>\n\n\n\n<div style=\"height:60px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\u0db6\u0dd0\u0dbd\u0dd6 \u0db6\u0dd0\u0dbd\u0dca\u0db8\u0da7 \u0dc3\u0d82\u0d9a\u0dd3\u0dbb\u0dca\u0dab \u0dc3\u0dd4\u0dc5\u0dd4 \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0d9a\u0dca \u0dad\u0dd2\u0dba\u0dd9\u0db1\u0dc0\u0dcf \u0dc0\u0d9c\u0dda \u0db4\u0dd9\u0db1\u0dd4\u0dab\u0dad\u0dca, \u0d94\u0dba\u0dcf\u0dbd\u0da7 \u0daf\u0dd0\u0db1\u0da7 \u0dad\u0dd2\u0dba\u0dd9\u0db1 \u0daf\u0dd0\u0db1\u0dd4\u0db8\u0dd9\u0db1\u0dca \u0db8\u0dda\u0d9a \u0db4\u0dc4\u0dc3\u0dd4\u0dc0\u0dd9\u0db1\u0dca \u0dc0\u0dd2\u0dc3\u0db3\u0d9c\u0db1\u0dca\u0db1 \u0db4\u0dd4\u0dc5\u0dd4\u0dc0\u0db1\u0dca.<\/p>\n\n\n\n<p>\u0d85\u0db4\u0dd2 \u0db8\u0dd4\u0dbd\u0dd2\u0db1\u0dca\u0db8<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}a=8+3\\sqrt{21}\\;\\text{\u0dc4\u0dcf}\\;b=8-3\\sqrt{21}\\;\\text{\u0dbd\u0dd9\u0dc3\u00a0\u0d9c\u0db1\u0dd2\u0db8\u0dd4.}\\\\\\sqrt[3]a\\in\\mathbb{R}\\;\\text{\u0dc4\u0dcf}\\;\\sqrt[3]b\\in\\mathbb{R}\\;\\text{\u0dc0\u0db1\u00a0\u0dc0\u0dd2\u0da7,\u00a0}\\;\\sqrt[3]a+\\sqrt[3]b\\in\\mathbb{R}\\;\\text{\u0dc0\u0dd2\u0dba\u00a0\u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.}\\end{array}<\/span><\/p>\n\n\n\n<p>\u2234 \u0d85\u0dc0\u0dc3\u0dcf\u0db1\u0dba\u0dda\u0daf\u0dd3 \u0dbd\u0dd0\u0db6\u0dd9\u0db1 \u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb \u0dad\u0dcf\u0dad\u0dca\u0dad\u0dca\u0dc0\u0dd2\u0d9a \u0dc3\u0d82\u0d9b\u0dca\u200d\u0dba\u0dcf\u0dc0\u0d9a\u0dca \u0dc0\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}x&amp;=&amp;\\sqrt[3]a+\\sqrt[3]b\\\\x^3&amp;=&amp;\\left(\\sqrt[3]a+\\sqrt[3]b\\right)^3\\\\x^3&amp;=&amp;a+3\\left(\\sqrt[3]a\\right)\\left(\\sqrt[3]b\\right)^2+3\\left(\\sqrt[3]a\\right)^2\\left(\\sqrt[3]b\\right)+b\\\\[4px]x^3&amp;=&amp;a+b+3\\sqrt[3]{ab^2}+3\\sqrt[3]{a^2b}\\\\[4px]x^3&amp;=&amp;a+b+3\\sqrt[3]{abb}+3\\sqrt[3]{aab}\\\\[8px]ab=ba&amp;=&amp;\\left(8+3\\sqrt{21}\\right)\\left(8-3\\sqrt{21}\\right)\\\\&amp;=&amp;8^2-\\left(3\\sqrt{21}\\right)^2\\\\&amp;=&amp;64-189\\\\&amp;=&amp;-125\\\\&amp;=&amp;\\left(-5\\right)^3\\\\[8px]x^3&amp;=&amp;a+b+3\\left(-5\\right)\\sqrt[3]b+3\\left(-5\\right)\\sqrt[3]a\\\\x^3&amp;=&amp;a+b-15\\left(\\sqrt[3]a+\\sqrt[3]b\\right)\\\\x^3&amp;=&amp;a+b-15x\\\\x^3&amp;=&amp;16-15x\\\\x^3+15x-16&amp;=&amp;0\\end{array}<\/span><\/p>\n\n\n\n<p>\u0db8\u0dd9\u0dc0\u0dd0\u0db1\u0dd2 x\u0dc4\u0dd2 \u0d9d\u0db1\u0dba\u0d9a\u0dca \u0d85\u0da9\u0d82\u0d9c\u0dd4 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba\u0d9a\u0dca \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8\u0dda\u0daf\u0dd3 x \u0da7 \u0dc3\u0dd4\u0dc0\u0dd2\u0dc1\u0dda\u0dc2\u0dd3 \u0d85\u0d9c\u0dba\u0dba\u0db1\u0dca \u0d9a\u0dd2\u0dc4\u0dd2\u0db4\u0dba\u0d9a\u0dca \u0d86\u0daf\u0dda\u0dc1 \u0d9a\u0dbb \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dad\u0dd8\u0db4\u0dca\u0dad \u0d9a\u0dbb\u0db1 \u0d85\u0d9c\u0dba \u0dc3\u0dd9\u0dc0\u0dd3\u0db8 \u0dc0\u0da9\u0dcf \u0db4\u0dc4\u0dc3\u0dd4 \u0dc0\u0dda.<\/p>\n\n\n\n<p>x=1 \u0dc0\u0db1 \u0dc0\u0dd2\u0da7 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dad\u0dd8\u0db4\u0dca\u0dad \u0dc0\u0db1 \u0db6\u0dd0\u0dc0\u0dd2\u0db1\u0dca, x =1 \u0db8\u0dd9\u0dc4\u0dd2 \u0d91\u0d9a\u0dca \u0dc0\u0dd2\u0dc3\u0db3\u0dd4\u0db8\u0d9a\u0dca \u0dc0\u0dda.<\/p>\n\n\n\n<p>\u0d91\u0db1\u0db8\u0dca, (x-1)\u0db8\u0dd9\u0dc4\u0dd2 \u0dc3\u0dcf\u0db0\u0d9a\u0dba\u0d9a\u0dca \u0dc0\u0dda.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\therefore\\left(x-1\\right)\\left(x^2+x+16\\right)=0<\/span><\/p>\n\n\n\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}x\\in\\mathbb{R}\\;\\text{\u0db1\u0dd2\u0dc3\u0dcf},\\;x=1\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\\\\\text{\u0d91\u0db1\u0db8\u0dca,\u00a0}\\;\\sqrt[3]a+\\sqrt[3]b&amp;=&amp;1\\\\\\sqrt[3]{8+3\\sqrt{21}}+\\sqrt[3]{8-3\\sqrt{21}}&amp;=&amp;1\\end{array}<\/span>\n\n\n\n<div style=\"height:60px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0db6\u0dd0\u0dbd\u0dd6 \u0db6\u0dd0\u0dbd\u0dca\u0db8\u0da7 \u0dc3\u0d82\u0d9a\u0dd3\u0dbb\u0dca\u0dab \u0dc3\u0dd4\u0dc5\u0dd4 \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0d9a\u0dca \u0dad\u0dd2\u0dba\u0dd9\u0db1\u0dc0\u0dcf \u0dc0\u0d9c\u0dda \u0db4\u0dd9\u0db1\u0dd4\u0dab\u0dad\u0dca, \u0d94\u0dba\u0dcf\u0dbd\u0da7 \u0daf\u0dd0\u0db1\u0da7 \u0dad\u0dd2\u0dba\u0dd9\u0db1 \u0daf\u0dd0\u0db1\u0dd4\u0db8\u0dd9\u0db1\u0dca \u0db8\u0dda\u0d9a \u0db4\u0dc4\u0dc3\u0dd4\u0dc0\u0dd9\u0db1\u0dca \u0dc0\u0dd2\u0dc3\u0db3\u0d9c\u0db1\u0dca\u0db1 \u0db4\u0dd4\u0dc5\u0dd4\u0dc0\u0db1\u0dca. \u0d85\u0db4\u0dd2 \u0db8\u0dd4\u0dbd\u0dd2\u0db1\u0dca\u0db8 \u2234 \u0d85\u0dc0\u0dc3\u0dcf\u0db1\u0dba\u0dda\u0daf\u0dd3 \u0dbd\u0dd0\u0db6\u0dd9\u0db1 \u0db4\u0dd2\u0dc5\u0dd2\u0dad\u0dd4\u0dbb \u0dad\u0dcf\u0dad\u0dca\u0dad\u0dca\u0dc0\u0dd2\u0d9a \u0dc3\u0d82\u0d9b\u0dca\u200d\u0dba\u0dcf\u0dc0\u0d9a\u0dca \u0dc0\u0dd2\u0dba \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2. \u0db8\u0dd9\u0dc0\u0dd0\u0db1\u0dd2 x\u0dc4\u0dd2 \u0d9d\u0db1\u0dba\u0d9a\u0dca \u0d85\u0da9\u0d82\u0d9c\u0dd4 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba\u0d9a\u0dca \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8\u0dda\u0daf\u0dd3 x \u0da7 \u0dc3\u0dd4\u0dc0\u0dd2\u0dc1\u0dda\u0dc2\u0dd3 \u0d85\u0d9c\u0dba\u0dba\u0db1\u0dca \u0d9a\u0dd2\u0dc4\u0dd2\u0db4\u0dba\u0d9a\u0dca \u0d86\u0daf\u0dda\u0dc1 \u0d9a\u0dbb \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dad\u0dd8\u0db4\u0dca\u0dad \u0d9a\u0dbb\u0db1 \u0d85\u0d9c\u0dba \u0dc3\u0dd9\u0dc0\u0dd3\u0db8 \u0dc0\u0da9\u0dcf \u0db4\u0dc4\u0dc3\u0dd4 \u0dc0\u0dda. x=1 \u0dc0\u0db1 \u0dc0\u0dd2\u0da7 \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab\u0dba \u0dad\u0dd8\u0db4\u0dca\u0dad \u0dc0\u0db1 \u0db6\u0dd0\u0dc0\u0dd2\u0db1\u0dca, x [&hellip;]<\/p>\n","protected":false},"author":64,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","footnotes":""},"categories":[42],"tags":[],"class_list":{"0":"post-21223","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-advanced-level-science"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/21223"}],"collection":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/users\/64"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/comments?post=21223"}],"version-history":[{"count":8,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/21223\/revisions"}],"predecessor-version":[{"id":21469,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/21223\/revisions\/21469"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=21223"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=21223"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=21223"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}