{"id":1600,"date":"2024-11-28T23:00:00","date_gmt":"2024-11-28T15:00:00","guid":{"rendered":"https:\/\/thereisno.top\/?p=1600"},"modified":"2024-11-28T23:04:46","modified_gmt":"2024-11-28T15:04:46","slug":"%e9%9f%a6%e8%be%be%e5%85%ac%e5%bc%8f%e6%8e%a8%e5%af%bc","status":"publish","type":"post","link":"https:\/\/thereisno.top\/?p=1600","title":{"rendered":"\u97e6\u8fbe\u516c\u5f0f\u63a8\u5bfc"},"content":{"rendered":"\n<p>\u4e00\u5143n\u6b21\u65b9\u7a0b <math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mtable><mtr><mtd columnalign=\"right\"><msub><mi>a<\/mi><mi>n<\/mi><\/msub><msup><mi>x<\/mi><mi>n<\/mi><\/msup><mo>+<\/mo><msub><mi>a<\/mi><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><msup><mi>x<\/mi><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msup><mo>+<\/mo><mi>.<\/mi><mi>.<\/mi><mi>.<\/mi><mo>+<\/mo><msub><mi>a<\/mi><mn>1<\/mn><\/msub><mi>x<\/mi><mo>+<\/mo><msub><mi>a<\/mi><mn>0<\/mn><\/msub><mo>=<\/mo><mn>0<\/mn><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\n\\begin{align}\na_nx^n + a_{n-1}x^{n-1} + &#8230; + a_1x + a_0 = 0\n\\end{align}\n<\/annotation><\/semantics><\/math> \u7684\u6839\u4e3a<math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo>,<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo>,<\/mo><mi>.<\/mi><mi>.<\/mi><mi>.<\/mi><mo>,<\/mo><msub><mi>x<\/mi><mi>n<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">x_1, x_2, &#8230;, x_n<\/annotation><\/semantics><\/math>\uff0c\u5176\u4e2d<math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>a<\/mi><mi>n<\/mi><\/msub><mo>\u2260<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">a_n \\neq 0<\/annotation><\/semantics><\/math>\u3002 \u90a3\u4e48(1)\u5f0f\u53ef\u4ee5\u5199\u6210\u4e0b\u9762\u7684\u5f62\u5f0f\uff1a <math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mtable><mtr><mtd columnalign=\"right\"><msub><mi>a<\/mi><mi>n<\/mi><\/msub><mrow><mo stretchy=\"true\" form=\"prefix\">(<\/mo><mi>x<\/mi><mo>\u2212<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo stretchy=\"true\" form=\"postfix\">)<\/mo><\/mrow><mrow><mo stretchy=\"true\" form=\"prefix\">(<\/mo><mi>x<\/mi><mo>\u2212<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo stretchy=\"true\" form=\"postfix\">)<\/mo><\/mrow><mi>.<\/mi><mi>.<\/mi><mi>.<\/mi><mrow><mo stretchy=\"true\" form=\"prefix\">(<\/mo><mi>x<\/mi><mo>\u2212<\/mo><msub><mi>x<\/mi><mi>n<\/mi><\/msub><mo stretchy=\"true\" form=\"postfix\">)<\/mo><\/mrow><mo>=<\/mo><mn>0<\/mn><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\n\\begin{align}\na_n(x &#8211; x_1)(x &#8211; x_2)&#8230;(x &#8211; x_n) = 0\n\\end{align}\n<\/annotation><\/semantics><\/math><\/p>\n<p>\u5c06\u5176\u5c55\u5f00,\u5e76\u89c2\u5bdf\u591a\u9879\u5f0f\u7cfb\u6570,<math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><msub><mi>x<\/mi><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">x_{n-1}<\/annotation><\/semantics><\/math>\u7684\u7cfb\u6570: <math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>\u2212<\/mo><mrow><mo stretchy=\"true\" form=\"prefix\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo>+<\/mo><mi>.<\/mi><mi>.<\/mi><mi>.<\/mi><mo>+<\/mo><msub><mi>x<\/mi><mi>n<\/mi><\/msub><mo stretchy=\"true\" form=\"postfix\">)<\/mo><\/mrow><msub><mi>a<\/mi><mi>n<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">-(x_1 + x_2 + &#8230; + x_n)a_n<\/annotation><\/semantics><\/math> \u5e38\u6570\u9879\uff1a <math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mrow><mo stretchy=\"true\" form=\"prefix\">(<\/mo><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"true\" form=\"postfix\">)<\/mo><\/mrow><mi>n<\/mi><\/msup><msub><mi>x<\/mi><mn>1<\/mn><\/msub><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mi>.<\/mi><mi>.<\/mi><mi>.<\/mi><msub><mi>x<\/mi><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><msub><mi>a<\/mi><mi>n<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">(-1)^nx_1x_2&#8230;x_{n-1}a_n<\/annotation><\/semantics><\/math><\/p>\n<p>\u6bd4\u8f83\u5e38\u6570\u9879\u548c<math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><msub><mi>x<\/mi><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><annotation encoding=\"application\/x-tex\">x_{n-1}<\/annotation><\/semantics><\/math>\u7684\u7cfb\u6570\uff0c\u53ef\u4ee5\u5f97\u5230\uff1a <math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mtable><mtr><mtd columnalign=\"right\"><msub><mi>a<\/mi><mn>0<\/mn><\/msub><\/mtd><mtd columnalign=\"left\"><mo>=<\/mo><msup><mrow><mo stretchy=\"true\" form=\"prefix\">(<\/mo><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"true\" form=\"postfix\">)<\/mo><\/mrow><mi>n<\/mi><\/msup><msub><mi>x<\/mi><mn>1<\/mn><\/msub><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mi>.<\/mi><mi>.<\/mi><mi>.<\/mi><msub><mi>x<\/mi><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><msub><mi>a<\/mi><mi>n<\/mi><\/msub><\/mtd><\/mtr><mtr><mtd columnalign=\"right\"><msub><mi>a<\/mi><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><\/mtd><mtd columnalign=\"left\"><mo>=<\/mo><mo>\u2212<\/mo><mrow><mo stretchy=\"true\" form=\"prefix\">(<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo>+<\/mo><mi>.<\/mi><mi>.<\/mi><mi>.<\/mi><mo>+<\/mo><msub><mi>x<\/mi><mi>n<\/mi><\/msub><mo stretchy=\"true\" form=\"postfix\">)<\/mo><\/mrow><msub><mi>a<\/mi><mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\n\\begin{aligned}\na_0 &amp;=(-1)^nx_1x_2&#8230;x_{n-1}a_n  \\\\ \na_{n-1} &amp;=-(x_1 + x_2 + &#8230; + x_n)a_n\n\\end{aligned}\n<\/annotation><\/semantics><\/math><\/p>\n<p><math display=\"inline\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mo>\u2234<\/mo><annotation encoding=\"application\/x-tex\">\\therefore<\/annotation><\/semantics><\/math> <math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mtable><mtr><mtd columnalign=\"right\"><\/mtd><mtd columnalign=\"left\"><munderover><mo>\u220f<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><msub><mi>x<\/mi><mi>i<\/mi><\/msub><mo>=<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mi>.<\/mi><mi>.<\/mi><mi>.<\/mi><msub><mi>x<\/mi><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><msub><mi>a<\/mi><mi>n<\/mi><\/msub><mo>=<\/mo><mfrac><mrow><msup><mrow><mo stretchy=\"true\" form=\"prefix\">(<\/mo><mo>\u2212<\/mo><mn>1<\/mn><mo stretchy=\"true\" form=\"postfix\">)<\/mo><\/mrow><mi>n<\/mi><\/msup><msub><mi>a<\/mi><mn>0<\/mn><\/msub><\/mrow><msub><mi>a<\/mi><mi>n<\/mi><\/msub><\/mfrac><\/mtd><\/mtr><mtr><mtd columnalign=\"right\"><\/mtd><mtd columnalign=\"left\"><munderover><mo>\u2211<\/mo><mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>n<\/mi><\/munderover><msub><mi>x<\/mi><mi>i<\/mi><\/msub><mo>=<\/mo><msub><mi>x<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>x<\/mi><mn>2<\/mn><\/msub><mo>+<\/mo><mi>.<\/mi><mi>.<\/mi><mi>.<\/mi><mo>+<\/mo><msub><mi>x<\/mi><mi>n<\/mi><\/msub><mo>=<\/mo><mo>\u2212<\/mo><mfrac><msub><mi>a<\/mi><mrow><mi>n<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mrow><\/msub><msub><mi>a<\/mi><mi>n<\/mi><\/msub><\/mfrac><\/mtd><\/mtr><\/mtable><annotation encoding=\"application\/x-tex\">\n\\begin{equation}\n\\begin{aligned}\n&amp;\\prod_{i=1}^nx_i=x_1x_2&#8230;x_{n-1}a_n=\\frac{(-1)^{n}{a_0}}{a_n} \\\\  \n&amp;\\sum_{i=1}^nx_i=x_1 + x_2 + &#8230; + x_n = -\\frac{a_{n-1}}{a_n}\n\\end{aligned}\n\\end{equation}\n<\/annotation><\/semantics><\/math><\/p>\n<p>\u8fd9\u5c31\u662f\u4e00\u5143n\u6b21\u65b9\u7a0b\u7684\u97e6\u8fbe\u516c\u5f0f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e00\u5143n\u6b21\u65b9\u7a0b anxn+an\u22121xn\u22121+&#8230;+a1x+a0=0 \\begin{align} a_nx^n  &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/thereisno.top\/?p=1600\" class=\"more-link\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">\u201c\u97e6\u8fbe\u516c\u5f0f\u63a8\u5bfc\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[91],"tags":[90],"class_list":["post-1600","post","type-post","status-publish","format-standard","hentry","category-91","tag-90"],"_links":{"self":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/1600","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1600"}],"version-history":[{"count":4,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/1600\/revisions"}],"predecessor-version":[{"id":1604,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/1600\/revisions\/1604"}],"wp:attachment":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1600"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1600"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}