{"id":21879,"date":"2025-09-21T22:55:46","date_gmt":"2025-09-21T14:55:46","guid":{"rendered":"https:\/\/blog.iyatt.com\/?p=21879"},"modified":"2025-09-21T23:33:07","modified_gmt":"2025-09-21T15:33:07","slug":"%e3%80%8a%e5%b7%a5%e7%a8%8b%e6%95%b0%e5%ad%a6-%e7%ba%bf%e6%80%a7%e4%bb%a3%e6%95%b0%e3%80%8b%e7%ac%ac%e5%85%ad%e7%89%88-%e4%b9%a0%e9%a2%98%e4%b8%80%ef%bc%88%e8%a1%8c%e5%88%97%e5%bc%8f-%ef%bc%89","status":"publish","type":"post","link":"https:\/\/blog.iyatt.com\/?p=21879","title":{"rendered":"\u300a\u5de5\u7a0b\u6570\u5b66 \u7ebf\u6027\u4ee3\u6570\u300b\u7b2c\u516d\u7248 \u4e60\u9898\u4e00\uff08\u884c\u5217\u5f0f \uff09 \u7b2c 6 \u9898 \u90e8\u5206\u8bc1\u660e"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/blog.iyatt.com\/?p=21879\/#%E7%AC%AC%EF%BC%882%EF%BC%89%E9%A2%98\" >\u7b2c\uff082\uff09\u9898<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/blog.iyatt.com\/?p=21879\/#%E7%AC%AC%EF%BC%884%EF%BC%89%E9%A2%98\" >\u7b2c\uff084\uff09\u9898<\/a><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"%E7%AC%AC%EF%BC%882%EF%BC%89%E9%A2%98\"><\/span>\u7b2c\uff082\uff09\u9898<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p>\u9898\u76ee<\/p>\n<pre><code class=\"language-katex\">\\begin{vmatrix}\nax+by&amp;ay+bz&amp;az+bx\\\\\nay+bz&amp;az+bx&amp;ax+by\\\\\naz+bx&amp;ax+by&amp;ay+bz\n\\end{vmatrix}\n=\n(a^3+b^3)\n\\begin{vmatrix}\nx&amp;y&amp;z\\\\\ny&amp;z&amp;x\\\\\nz&amp;x&amp;y\n\\end{vmatrix}<\/code><\/pre>\n<p>\u8bc1\u660e<\/p>\n<pre><code class=\"language-katex\">\\begin{aligned}\n\\begin{vmatrix}\nax+by&amp;ay+bz&amp;az+bx\\\\\nay+bz&amp;az+bx&amp;ax+by\\\\\naz+bx&amp;ax+by&amp;ay+bz\n\\end{vmatrix}\n\n&amp;\\xlongequal[\u7136\u540e\u5206\u522b\u63d0\u51fa\u7b2c1\u5217\u7684\u516c\u56e0\u5f0f]{\u5148\u62c6\u7b2c1\u5217\uff0c\u53d8\u4e3a\u4e24\u4e2a\u884c\u5217\u5f0f\u76f8\u52a0}\na\\begin{vmatrix}\nx&amp;ay+bz&amp;az+bx\\\\\ny&amp;az+bx&amp;ax+by\\\\\nz&amp;ax+by&amp;ay+bz\n\\end{vmatrix}\n+\nb\\begin{vmatrix}\ny&amp;ay+bz&amp;az+bx\\\\\nz&amp;az+bx&amp;ax+by\\\\\nx&amp;ax+by&amp;ay+bz\n\\end{vmatrix} \\\\\n\n&amp;\\xlongequal[\u51fa\u73b0\u4e24\u5217\u5143\u7d20\u76f8\u7b49\u7684\u884c\u5217\u5f0f\u503c\u4e3a0]{\u524d\u4e00\u4e2a\u62c6\u7b2c3\u5217\uff0c\u540e\u4e00\u4e2a\u62c6\u7b2c2\u5217}\na^2\\begin{vmatrix}\nx&amp;ay+bz&amp;z\\\\\ny&amp;az+bx&amp;x\\\\\nz&amp;ax+by&amp;y\n\\end{vmatrix}\n+\nb^2\\begin{vmatrix}\ny&amp;z&amp;az+bx\\\\\nz&amp;x&amp;ax+by\\\\\nx&amp;y&amp;ay+bz\n\\end{vmatrix} \\\\\n\n&amp;\\xlongequal[]{\u7ee7\u7eed\u62c6\u5404\u81ea\u5269\u4e0b\u7684\u4e00\u5217}\na^3\\begin{vmatrix}\nx&amp;y&amp;z\\\\\ny&amp;z&amp;x\\\\\nz&amp;x&amp;y\n\\end{vmatrix}\n+\nb^3\\begin{vmatrix}\ny&amp;z&amp;x\\\\\nz&amp;x&amp;y\\\\\nx&amp;y&amp;z\n\\end{vmatrix} \\\\\n&amp;\\xlongequal[\u540e\u4e00\u4e2a\u884c\u5217\u5f0f\u4e92\u6362\u4e24\u6b21\u7b26\u53f7\u4e0d\u53d8]{\u884c\u5217\u5f0f\u4e92\u6362\u5217\uff0c\u7b26\u53f7\u76f8\u53cd}\na^3\\begin{vmatrix}\nx&amp;y&amp;z\\\\\ny&amp;z&amp;x\\\\\nz&amp;x&amp;y\n\\end{vmatrix}\n+\nb^3\\begin{vmatrix}\nx&amp;y&amp;z\\\\\ny&amp;z&amp;x\\\\\nz&amp;x&amp;y\n\\end{vmatrix} \\\\\n\n&amp;=\n(a^3+b^3)\\begin{vmatrix}\nx&amp;y&amp;z\\\\\ny&amp;z&amp;x\\\\\nz&amp;x&amp;y\n\\end{vmatrix}\n\\end{aligned}<\/code><\/pre>\n<h1><span class=\"ez-toc-section\" id=\"%E7%AC%AC%EF%BC%884%EF%BC%89%E9%A2%98\"><\/span>\u7b2c\uff084\uff09\u9898<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p>\u9898\u76ee<\/p>\n<pre><code class=\"language-katex\">\\begin{vmatrix}\n1&amp;1&amp;1&amp;1\\\\\na&amp;b&amp;c&amp;d\\\\\na^2&amp;b^2&amp;c^2&amp;d^2\\\\\na^4&amp;b^4&amp;c^4&amp;d^4\n\\end{vmatrix}\n=\n(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)(a+b+c+d)<\/code><\/pre>\n<p>\u8bc1\u660e<\/p>\n<pre><code class=\"language-katex\">\\begin{array}{l}\n\u8bbe\u9898\u76ee\u7684\u884c\u5217\u5f0f\u4e3aA,\n\u5c06A\u884c\u5217\u5f0f\u6269\u5145\u4e3a5\u9636\u884c\u5217\u5f0f B=\n\\begin{vmatrix}\n1&amp;1&amp;1&amp;1&amp;1\\\\\na&amp;b&amp;c&amp;d&amp;x\\\\\na^2&amp;b^2&amp;c^2&amp;d^2&amp;x^2\\\\\na^3&amp;b^3&amp;c^3&amp;d^3&amp;x^3\\\\\na^4&amp;b^4&amp;c^4&amp;d^4&amp;x^4\n\\end{vmatrix} \\\\\n\n\u5c06B\u6309\u7b2c5\u5217\u5c55\u5f00\\\\\n\\begin{aligned}\nB&amp;=(-1)^{1+5}\\times1\\times M_{15}+(-1)^{2+5}M_{25}x+(-1)^{3+5}M_{35}x^2+(-1)^{4+5}M_{45}x^3+(-1)^{5+5}M_{55}x^4\\\\\n&amp;=M_{15}-M_{25}x+M_{35}x^2-M_{45}x^3+M_{55}x^4\n\\end{aligned} \\\\\n\n\u53ef\u4ee5\u53d1\u73b0 A=M_{45}=\n\\begin{vmatrix}\n1&amp;1&amp;1&amp;1\\\\\na&amp;b&amp;c&amp;d\\\\\na^2&amp;b^2&amp;c^2&amp;d^2\\\\\na^4&amp;b^4&amp;c^4&amp;d^4\n\\end{vmatrix}\uff0c\u800cM_{45}\u662fx^3\u9879\u7cfb\u6570\u7684\u76f8\u53cd\u6570\n\n\\\\ \\\\\n\nB\u662f\u4e00\u4e2a\u8303\u5fb7\u8499\u884c\u5217\u5f0f\uff0c\u6709\\\\\n\\begin{aligned}\nB&amp;=(b-a)(c-a)(d-a)(x-a)(c-b)(d-b)(x-b)(d-c)(x-c)(x-d)\\\\\n&amp;=(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)[(x-a)(x-b)(x-c)(x-d)]\\\\\n&amp;\\xlongequal{\u542bx\u9879\u8868\u793a\u4e3a\u4e00\u822c\u5f0f}(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)(D_0x^0+D_1x+D_2x^2+D_3x^3+D_4x^4]) \\\\\n&amp;\\xlongequal{\u548c\u6309\u5217\u5c55\u5f00\u5f0f\u76f8\u7b49}M_{15}-M_{25}x+M_{35}x^2-M_{45}x^3+M_{55}x^4\n\\end{aligned} \\\\\n\n\u90a3\u4e48\u6709\n(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)\\cdot D_3x^3=-M_{45}x^3 \\\\\n\u5373A=M_{45}=-(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)D_3\\\\\n\u8ba1\u7b97\u53ef\u5f97D_3=-(a+b+c+d) \\\\ \\\\\n\n\u5219\u8bc1\u660eA=(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)(a+b+c+d)\n\\end{array}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u7b2c\uff082\uff09\u9898 \u9898\u76ee \\begin{vmatrix} ax+by&amp;ay+bz&amp;az+bx\\\\ ay [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"_lmt_disableupdate":"no","_lmt_disable":"no","footnotes":""},"categories":[1,612],"tags":[950,944,1628,1622,1755,1754],"class_list":["post-21879","post","type-post","status-publish","format-standard","hentry","category-all","category-612","tag-950","tag-944","tag-1628","tag-1622","tag-1755","tag-1754"],"modified_by":"IYATT-yx","_links":{"self":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21879","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=21879"}],"version-history":[{"count":7,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21879\/revisions"}],"predecessor-version":[{"id":21886,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21879\/revisions\/21886"}],"wp:attachment":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=21879"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=21879"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=21879"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}