{"id":632,"date":"2024-02-06T16:48:31","date_gmt":"2024-02-06T08:48:31","guid":{"rendered":"https:\/\/big-tan.top\/?p=632"},"modified":"2024-02-13T12:11:25","modified_gmt":"2024-02-13T04:11:25","slug":"%e5%9b%a0%e5%bc%8f%e5%88%86%e8%a7%a3%e6%8a%80%e5%b7%a7%e9%9b%86%e9%94%a6%ef%bc%88%e4%ba%8c%ef%bc%89","status":"publish","type":"post","link":"https:\/\/itantan.eu.org\/?p=632","title":{"rendered":"\u56e0\u5f0f\u5206\u89e3\u6280\u5de7\u96c6\u9526\uff08\u4e8c\uff09"},"content":{"rendered":"\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-93eaab0 stk-block-background\" data-block-id=\"93eaab0\"><style>.stk-93eaab0{background-color:#F6F6F6 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-93eaab0:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-93eaab0-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-bb90bb8\" data-v=\"4\" data-block-id=\"bb90bb8\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-bb90bb8-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-bb90bb8-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-93c3547\" data-block-id=\"93c3547\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e00\uff1a\u56e0\u5f0f\u5206\u89e3$x^4-2x^2y-3y^2+8y-4$\u30021977\u5e74\u9ad8\u8003\u9898\uff0c\u5f53\u5e74\u96be\u4f4f\u4e0d\u5c11\u8003\u751f\uff0c\u5982\u4eca\u521d\u4e2d\u77e5\u8bc6\u7b80\u5355\u6c42\u89e3\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u901a\u8fc7\u89c2\u5bdf\u53d1\u73b0\uff0c\u524d\u4e24\u9879\u53ef\u4ee5\u8bbe\u6cd5\u51d1\u6210\u5b8c\u5168\u5e73\u65b9\uff0c\u901a\u8fc7\u589e\u51cf\u9879\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u89e3\u9898\u6b65\u9aa4\u4e2d\u89c4\u4e2d\u77e9\uff0c\u4e0d\u9700\u8981\u7279\u522b\u6280\u5de7\u3002<br><br>$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\\text{\u539f\u5f0f=}(x^2)^2-2x^2y+y^2-4y^2+8y-4\\\\&amp;=(x^2-y)^2-(4y^2-8y+4)\\\\&amp;=(x^2-y)^2-(2y-2)^2\\\\&amp;=(x^2-y+2y-2)(x^2-y-2y+2)\\\\&amp;=(x^2+y-2)(x^2-3y+2)\\end{split}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-e574b1e stk-block-background\" data-block-id=\"e574b1e\"><style>.stk-e574b1e{background-color:#ffe2c7 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-e574b1e:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-e574b1e-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-5313ad3\" data-v=\"4\" data-block-id=\"5313ad3\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-5313ad3-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-5313ad3-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-a3c67eb\" data-block-id=\"a3c67eb\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e8c\uff1a\u56e0\u5f0f\u5206\u89e3$x^3-6x-4$\u3002\u96be\u4f4f\u4e0d\u5c11\u540c\u5b66\uff0c\u5176\u5b9e\u5c31\u662f\u516c\u5f0f\u4e0d\u719f\u7ec3\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u89c2\u5bdf\u53d1\u73b0\uff0c\u6709\u4e09\u6b21\u65b9\uff0c\u7acb\u5373\u60f3\u5230\u53ef\u4ee5\u4f7f\u7528\u7acb\u65b9\u548c\u5dee\u516c\u5f0f\uff0c\u7531\u4e8e\u5e38\u6570\u9879\u662f4\uff0c\u53ef\u4ee5\u901a\u8fc7\u52a0\u51cf\u5e38\u6570\u6765\u51d1\u6210\u7acb\u65b9\u548c\u516c\u5f0f\uff0c\u7136\u540e\u5728\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002\u53e6\u5916\uff0c\u4e5f\u53ef\u4ee5\u901a\u8fc7\u524d\u4e24\u9879\u51d1\u5e73\u65b9\u5dee\u516c\u5f0f\u7684\u601d\u8def\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u96be\u5ea6\u4e5f\u4e0d\u5927\u3002<br><br>$\\begin{split}\\text{\u89e3\u6cd5\u4e00\uff1a}\\\\&amp;\\text{\u539f\u5f0f=}x^3+8-6x-12\\\\&amp;=(x+2)(x^2-2x+4)-6(x+2)\\\\&amp;=(x+2)(x^2-2x+4-6)\\\\&amp;=(x+2)(x^2-2x-2)\\end{split}$<br><br>$\\begin{split}\\text{\u89e3\u6cd5\u4e8c\uff1a}\\\\&amp;\\text{\u539f\u5f0f=}x^3-4x-2x-4\\\\&amp;=x(x^2-4)-2(x+2)\\\\&amp;=x(x+2)(x-2)-2(x+2)\\\\&amp;=(x+2)(x^2-2x-2)\\end{split}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-3bc4b66 stk-block-background\" data-block-id=\"3bc4b66\"><style>.stk-3bc4b66{background-color:#F6F6F6 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-3bc4b66:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-3bc4b66-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-c0318c4\" data-v=\"4\" data-block-id=\"c0318c4\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-c0318c4-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-c0318c4-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-79eebad\" data-block-id=\"79eebad\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e09\uff1a\u56e0\u5f0f\u5206\u89e3$x^5+x+1$\u3002\u770b\u4f3c\u65e0\u4ece\u4e0b\u624b\uff0c\u4f46\u53ea\u8981\u638c\u63e1\u6dfb\u9879\u6280\u5de7\uff0c\u7c7b\u4f3c\u9898\u76ee\u6613\u5982\u7ffb\u638c\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u89c2\u5bdf\u53d1\u73b0\uff0c\u7b2c\u4e00\u9879\u662f\u4e94\u6b21\u65b9\u3001\u7b2c\u4e8c\u9879\u662f\u4e00\u6b21\u65b9\uff0c\u5e38\u6570\u662f1\uff0c\u9996\u5148\u60f3\u5230\u7684\u65b9\u6cd5\u5c31\u662f\u964d\u6b21\uff0c\u5982\u4f55\u964d\u6b21\uff1f\u5fc5\u987b\u501f\u52a9\u6865\u6881\uff0c\u901a\u8fc7\u6dfb\u9879\u3001\u51cf\u9879\u8fdb\u884c\u964d\u6b21\u53d8\u6362\uff0c\u4ee5\u6b64\u4f5c\u4e3a\u7a81\u7834\u53e3\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002<br><br>$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\\text{\u539f\u5f0f=}x^5-x^2+x^2+x+1\\\\&amp;=x^2(x^3-1)+x^2+x+1\\\\&amp;=x^2(x-1)(x^2+x+1)+(x^2+x+1)\\\\&amp;=(x^2+x+1)(x^3-x^2+1)\\end{split}$<br><br><br>\u2003\u2003<strong>$\\bbox[yellow,8pt,border:2px solid red]{\\text{\u62d3\u5c55\u601d\u7ef4\u9898\uff1a\u56e0\u5f0f\u5206\u89e3\uff1a}a^4-4a+3}$<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u89c2\u5bdf\u53d1\u73b0\u6700\u9ad8\u6b21\u9879\u662f\u56db\u6b21\u9879\uff0c\u5176\u6b21\u5c31\u662f\u4e00\u6b21\u9879\uff0c\u9996\u5148\u60f3\u5230\u901a\u8fc7\u6dfb\u9879\u3001\u51cf\u9879\u51d1\u6210\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u8fdb\u884c\u964d\u6b21\u53d8\u6362\uff0c\u4ee5\u6b64\u4f5c\u4e3a\u7a81\u7834\u53e3\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002\u7c7b\u4f3c\u60c5\u51b5\u9ad8\u6b21\u9879\u901a\u5e38\u9700\u8981\u51d1\u6210\u5e73\u65b9\u5dee\u3002<br>$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\\text{\u539f\u5f0f}=(a^2)^2-2a^2+1+2a^2-4a+2\\\\&amp;=(a^2-1)^2+2(a^2-2a+1)\\\\&amp;=(a+1)^2\\cdot(a-1)^2+2(a-1)^2\\\\&amp;=(a-1)^2[(a+1)^2+2]\\\\&amp;=(a-1)^2(a^2+2a+3)\\end{split}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-02011ff stk-block-background\" data-block-id=\"02011ff\"><style>.stk-02011ff{background-color:#ffe2c7 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-02011ff:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-02011ff-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-bc1d176\" data-v=\"4\" data-block-id=\"bc1d176\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-bc1d176-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-bc1d176-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-0e8f924\" data-block-id=\"0e8f924\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u56db\uff1a\u56e0\u5f0f\u5206\u89e3$x^2-120x+3456$\u3002\u770b\u7740\u633a\u5413\u4eba\uff0c\u5176\u5b9e\u975e\u5e38\u7b80\u5355\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u5982\u679c\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\uff0c\u4e0d\u662f\u592a\u597d\u770b\u51fa\u6765\u7ed3\u679c\uff0c\u56e0\u4e3a\u5e38\u6570\u9879\u6bd4\u8f83\u5927\u3002\u53ef\u4ee5\u901a\u8fc7\u51d1\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u7684\u601d\u8def\u8fdb\u884c\u5206\u89e3\uff0c\u5e38\u6570\u9879\u53ef\u4ee5\u5206\u89e3\u4e3a\u4e24\u4e2a\u6570\u5b57\uff0c\u76ee\u7684\u5c31\u662f\u4e3a\u4e86\u51d1\u6210\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\uff0c\u672c\u8d28\u4e0a\u4e0e\u5341\u5b57\u9879\u4e58\u6cd5\u5f02\u66f2\u540c\u5de5\u3002<br><br>$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\\text{\u539f\u5f0f=}(x-60)^2-144\\\\&amp;=(x-60)^2-12^2\\\\&amp;=(x-60+12)(x-60-12)\\\\&amp;=(x-48)(x-72)\\end{split}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-e20ba81 stk-block-background\" data-block-id=\"e20ba81\"><style>.stk-e20ba81{background-color:#F6F6F6 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-e20ba81:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-e20ba81-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-573d3c1\" data-v=\"4\" data-block-id=\"573d3c1\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-573d3c1-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-573d3c1-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-8495911\" data-block-id=\"8495911\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e94\uff1a\u56e0\u5f0f\u5206\u89e3$x^3+(x^2-3x+4)^2+2$\u3002\u5b66\u4e60\u62c9\u739b\u52aa\u91d1\u77aa\u773c\u6cd5\uff01\u6709\u7684\u65f6\u5019\uff0c\u5206\u89e3\u56e0\u5f0f\u4e5f\u662f\u9700\u8981\u7b2c\u516d\u611f\u89c9\u7684\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u4e4d\u4e00\u770b\uff0c\u4f3c\u4e4e\u65e0\u6cd5\u4e0b\u624b\uff0c\u5c55\u5f00\u62ec\u53f7\u91cc\u9762\u7684\u591a\u9879\u5f0f\u6709\u56db\u6b21\u65b9\uff0c\u66f4\u662f\u65e0\u6cd5\u5206\u89e3\u4e86\u3002\u600e\u4e48\u529e\u5462\uff1f\u6211\u4eec\u53ea\u80fd\u4ece\u5e38\u65702\u5f00\u59cb\u8003\u8651\uff0c\u60f3\u529e\u6cd5\u628a\u8fd9\u4e2a2\u53d8\u6210\u4e24\u4e2a\u6570\uff0c\u4e00\u4e2a\u53ef\u4ee5\u548c$x^3$\u8fdb\u884c\u5206\u89e3\u56e0\u5f0f\uff0c\u4e00\u4e2a\u53ef\u4ee5\u548c\u62ec\u53f7\u91cc\u9762\u7684\u90a3\u4e00\u4e32\u8fdb\u884c\u5206\u89e3\uff0c\u5982\u4f55\u62c6\u5206\u8fd9\u4e2a\u5e38\u65702\u5462\uff1f\u7a81\u7136\u60f3\u5230$27-25=2\uff0c27=3^3\uff0c25=5^2$\uff0c\u4e5f\u8bb8\u8fd9\u6837\u53ef\u4ee5\uff1f\u975e\u8981\u7ed9\u8fd9\u79cd\u62c6\u5206\u6574\u6570\u7684\u65b9\u6cd5\u8d77\u4e2a\u540d\u5b57\u7684\u8bdd\uff0c\u4e0d\u59a8\u53eb\u4ed6\u62c9\u739b\u52aa\u91d1\u77aa\u773c\u6cd5\uff01\u62c9\u739b\u52aa\u91d1\u662f\u6570\u5b66\u5929\u624d\uff0c\u636e\u8bf4\u7279\u522b\u5584\u4e8e\u5bf9\u6574\u6570\u8fdb\u884c\u5de7\u5999\u7684\u53d8\u5f62\u3002<br><br>$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\\text{\u539f\u5f0f=}x^3+27-25+(x^2-3x+3)\\\\&amp;=x^3+3^3+(x^2-3x+4)^2-5^2\\\\&amp;=(x+3)(x^2-3x+9)+(x^2-3x+4+5)(x^2-3x+4-5)\\\\&amp;=(x+3)(x^2-3x+9)+(x^2-3x+9)(x^2-3x-1)\\\\&amp;=(x^2-3x+9)(x^2-2x+2)\\end{split}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-2c42877 stk-block-background\" data-block-id=\"2c42877\"><style>.stk-2c42877{background-color:#ffe2c7 !important;border-top-left-radius:18px !important;border-top-right-radius:18px !important;border-bottom-right-radius:18px !important;border-bottom-left-radius:18px !important;border-style:solid !important;overflow:auto !important}.stk-2c42877:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-2c42877-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-049fe14\" data-v=\"4\" data-block-id=\"049fe14\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-049fe14-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-049fe14-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-03b07d8\" data-block-id=\"03b07d8\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u516d\uff1a\u5206\u89e3\u56e0\u5f0f$a^5+b^5-(a+b)^5$\u3002\u4fc4\u56fd\u521d\u4e2d\u8003\u8bd5\u9898\uff0c\u8c01\u8bf4\u56fd\u5916\u6570\u5b66\u7b80\u5355\uff0c\u8fd9\u79cd\u56e0\u5f0f\u5206\u89e3\u4e5f\u6709\u4e9b\u751f\u731b\uff01<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u8fd9\u79cd\u9898\u76ee\u770b\u4f3c\u751f\u731b\uff0c\u5176\u5b9e\u6280\u5de7\u6027\u5e76\u4e0d\u662f\u5f88\u5f3a\uff0c\u4e3b\u8981\u8003\u5bdf\u516c\u5f0f\u8bb0\u5fc6\uff0c\u4e0d\u4ec5\u9700\u8981\u8bb0\u4f4f\u5e73\u65b9\u516c\u5f0f\u3001\u7acb\u65b9\u516c\u5f0f\u3001\u8fd8\u9700\u8981\u8bb0\u4f4f\u56db\u6b21\u65b9\u3001\u4e94\u6b21\u65b9\u7684\u76f8\u5173\u516c\u5f0f\uff0c\u53ea\u8981\u516c\u5f0f\u8bb0\u5f97\u7262\uff0c\u4ee3\u5165\u5373\u53ef\u3002<br><br>$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;{\u539f\u5f0f=}(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)-(a+b)(a+b)^4\\\\&amp;=(a+b)\\left[a^4-a^3b+a^2b^2-ab^3+b^4-(a+b)^4\\right]\\\\&amp;=(a+b)\\left[(a^4-a^3b+a^2b^2-ab^3+b^4)-(a^4+4a^3b+6a^2b^2+4ab^3+b^4)\\right]\\\\&amp;=(a+b)(-5a^3b-5a^2b^2-5ab^3)\\\\&amp;=-5ab(a+b)(a^2+ab+b^2)\\end{split}$<br><br><br>\u2003\u2003<strong>$\\bbox[yellow,8pt,border:2px solid red]{\\text{\u62d3\u5c55\u601d\u7ef4\u9898\uff1a\u56e0\u5f0f\u5206\u89e3\uff1a}a^6+4a^3-1}$\uff0c\u8fd9\u662f\u4e00\u9053\u6bd4\u8f83\u96be\uff0c\u4f46\u662f\u89e3\u6cd5\u5de7\u5999\u7684\u9898\u76ee\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u8fd9\u79cd\u7c7b\u578b\u7684\u56e0\u5f0f\u5206\u89e3\uff0c\u5e38\u89c1\u7684\u65b9\u6cd5\u90fd\u4e0d\u884c\uff0c\u65e0\u8bba\u662f\u8bd5\u63a2\u6cd5\u3001\u5206\u7ec4\u6cd5\u90fd\u6ca1\u6709\u529e\u6cd5\u8fdb\u884c\u5206\u89e3\uff0c\u8fd9\u91cc\u9700\u8981\u4f7f\u7528\u56e0\u5f0f\u5206\u89e3\u7684\u53e6\u5916\u4e00\u79cd\u65b9\u6cd5\uff1a\u6c42\u6839\u6cd5\u3002\u5148\u6c42\u51fa\u5176\u4e2d\u7684\u4e00\u4e2a\u56e0\u5b50\uff0c\u7136\u540e\u901a\u8fc7\u7efc\u5408\u9664\u6cd5\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002<br><br>$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\\text{\u8bbe\u539f\u5f0f\u4e3a\u65b9\u7a0b\uff1a}(a^3)^2+4a^3-1=0\\ldots(1)\\\\&amp;\\text{\u5c06$a^3$\u770b\u6210\u6574\u4f53\uff0c\u53ef\u4ee5\u6c42\u51fa\uff1a}a^3=-2\\pm\\sqrt5\\\\&amp;\u5047\u5b9ax\u3001y\u662f\u539f\u65b9\u7a0b\u5f0f(1)\u7684\u4e24\u4e2a\u6839\uff0c\u5219\u6709\uff1a\\begin{cases}x^3=-2+\\sqrt5\\\\[2ex]y^3=-2-\\sqrt5\\end{cases}\\Rightarrow x^3\\cdot y^3=-1\\Rightarrow xy=-1\\ldots(2)\\\\&amp;\\because x^3+y^3=-4\\Rightarrow x^3+y^3=(x+y)(x^2+y^2-xy)=(x+y)\\left[(x+y)^2-3xy\\right]\\ldots(3)\\\\&amp;\u4ee4x+y=t\uff0c\u5219(3)\u5f0f\u6362\u5143\u540e\u53ef\u5f97\uff1at(t^2+3)=-4\\ldots(4)\\\\&amp;\\because \u901a\u8fc7\u8bd5\u63a2\u6cd5\u53ef\u4ee5\u770b\u51fa\u6765t=-1\u662f\u65b9\u7a0b\u5f0f(4)\u7684\u4e00\u4e2a\u6839\uff0c\u4e5f\u5c31\u662f\u8bf4(4)\u5f0f\u5de6\u8fb9\u4e00\u5b9a\u5305\u542bt+1\u8fd9\u4e2a\u56e0\u5b50\\\\&amp;\\therefore t^3+3t+4=0\\Rightarrow t^3+1+3t+3=0\\Rightarrow (t+1)(t^2-t+1)+3(t+1)=0\\\\&amp;\\therefore (t+1)(t^2-t+4)=0\\\\&amp;\u663e\u7136t^2-t+4=0\u7684\\Delta=-\\sqrt{15}\\lt0\uff0c\u65e0\u5b9e\u6839\\\\&amp;\\therefore t=-1\\\\&amp;\\therefore x+y=-1\uff0cxy=-1\\\\&amp;\\therefore x\u3001y\u662f\u65b9\u7a0ba^2+a-1=0\u7684\u4e24\u4e2a\u6839\u3002\\\\&amp;\\because  x\u3001y\u540c\u65f6\u4e5f\u662f(1)\u5f0f\u65b9\u7a0b\u7684\u4e24\u4e2a\u6839\\\\&amp;\\therefore (1)\u5f0f\u5de6\u8fb9\u5fc5\u7136\u5305\u542ba^2+a-1\u8fd9\u4e2a\u56e0\u5b50\u3002\\\\&amp;\\therefore\u901a\u8fc7\u7efc\u5408\u9664\u6cd5\uff0c\u53ef\u5f97\uff1a\u539f\u5f0f=(a^2+a-1)(a^4-a^3+2a^2+a+1)\\end{split}$<\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u2003\u2003\u9898\u76ee\u4e00\uff1a\u56e0\u5f0f\u5206\u89e3$x^4-2x^2y-3y^2+8y-4$\u30021977\u5e74\u9ad8\u8003\u9898\uff0c\u5f53\u5e74\u96be\u4f4f\u4e0d\u5c11\u8003\u751f\uff0c\u5982\u4eca\u521d\u4e2d\u77e5 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,4],"tags":[],"class_list":["post-632","post","type-post","status-publish","format-standard","hentry","category-3","category-4"],"_links":{"self":[{"href":"https:\/\/itantan.eu.org\/index.php?rest_route=\/wp\/v2\/posts\/632","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/itantan.eu.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/itantan.eu.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=632"}],"version-history":[{"count":0,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=\/wp\/v2\/posts\/632\/revisions"}],"wp:attachment":[{"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=632"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=632"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=632"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}