{"id":621,"date":"2024-02-04T17:30:54","date_gmt":"2024-02-04T09:30:54","guid":{"rendered":"https:\/\/big-tan.top\/?p=621"},"modified":"2024-02-04T17:50:56","modified_gmt":"2024-02-04T09:50:56","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%b8%80%ef%bc%89","status":"publish","type":"post","link":"https:\/\/itantan.eu.org\/?p=621","title":{"rendered":"\u56e0\u5f0f\u5206\u89e3\u6280\u5de7\u96c6\u9526\uff08\u4e00\uff09"},"content":{"rendered":"\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-acf5002 stk-block-background\" data-block-id=\"acf5002\"><style>.stk-acf5002{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-acf5002:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-acf5002-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-baa9a9a\" data-v=\"4\" data-block-id=\"baa9a9a\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-baa9a9a-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-baa9a9a-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-2cba035\" data-block-id=\"2cba035\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e00\uff1a\u56e0\u5f0f\u5206\u89e3$x^{10}+x^2+1$\uff0c\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u9898\uff0c\u6709\u96be\u5ea6\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u9ad8\u6b21\u9879\u662f10\uff0c\u4e00\u822c\u6765\u8bf4\u9ad8\u6b21\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\u9700\u8981\u91c7\u7528\u6362\u5143\u6cd5\u964d\u5e42\uff0c\u5343\u65b9\u767e\u8ba1\u5229\u7528\u7acb\u65b9\u548c\u5dee\u516c\u5f0f\u3001\u5e73\u65b9\u548c\u5dee\u516c\u5f0f\u53d8\u5f62\uff0c\u7136\u540e\u5206\u89e3\u3002<br><br>$\\begin{split}\u89e3\uff1a\\\\&amp;\u8bbex^2=a\\\\&amp;\u539f\u5f0f=a^5+a+1\\\\&amp;=a^5-a^2+a^2+a+1\\\\&amp;=a^2(a^3-1)+(a^2+a+1)\\\\&amp;=a^2(a^3-1)+(a^2+a+1)\\\\&amp;=a^2(a-1)(a^2+a+1)+(a^2+a+1)\\\\&amp;=(a^2+a+1)(a^3-a^2+1)\\\\&amp;\\therefore\u539f\u5f0f=(x^4+x^2+1)(x^6-x^4+1)\\\\&amp;=[(x^2+1)^2-x^2](x^6-x^4+1)\\\\&amp;\\therefore (x^2+x+1)(x^2-x+1)(x^6-x^4+1)\\end{split}$<br><br>\u2003\u2003<strong>\u62d3\u5c55\u9898\uff1a\u56e0\u5f0f\u5206\u89e3$x^4-7x^2+1$\uff0c\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u9898\u76ee\uff0c\u770b\u4f3c\u7b80\u5355\uff0c\u96be\u5012\u5b66\u9738\u3002<\/strong><br>$\\begin{split}\u89e3\uff1a\\\\&amp;\u539f\u5f0f=(x^2)^2+1^2+2x^2-2x^2-7x^2\\\\&amp;=(x^2+1)^2=9x^2\\\\&amp;=(x^2+1)^2-(3x)^2\\\\&amp;=(x^2+1+3x)(x^2+1-3x)\\\\&amp;=(x^2+3x+1)(x^2-3x+1)\\end{split}$<\/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-d6977b3 stk-block-background\" data-block-id=\"d6977b3\"><style>.stk-d6977b3{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-d6977b3:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-d6977b3-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-abfdf53\" data-v=\"4\" data-block-id=\"abfdf53\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-abfdf53-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-abfdf53-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-bfef897\" data-block-id=\"bfef897\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e8c\uff1a\u56e0\u5f0f\u5206\u89e3$\\displaystyle(x^3+x^2+x+1)^2-x^3$\uff0c\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u9898\u76ee\uff0c\u96be\u5ea6\u6781\u5927\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u4e4d\u4e00\u770b\uff0c\u53ef\u4ee5\u5c55\u5f00\u540e\u5206\u89e3\uff0c\u4f46\u662f\u901a\u8fc7\u89c2\u5bdf\u53d1\u73b0\uff0c\u6709\u5e73\u65b9\u3001\u6709\u7acb\u65b9\uff0c\u53ef\u4ee5\u901a\u8fc7\u53d8\u6362\u6784\u9020\u5e73\u65b9\u5dee\u3001\u7acb\u65b9\u5dee\u516c\u5f0f\uff0c\u8fdb\u800c\u6c42\u89e3\u3002<br><br>$\\begin{split}\u89e3\uff1a\\\\&amp;\u539f\u5f0f=(x^3+x^2+x+1)^2-1-(x^3-1)\\\\&amp;=(x^3+x^2+x+1+1)(x^3+x^2+x+1-1)-(x-1)(x^2+x+1)\\\\&amp;=(x^3+x^2+x+2)(x^3+x^2+x)-(x-1)(x^2+x+1)\\\\&amp;=x(x^2+x+1)(x^3+x^2+x+2)-(x-1)(x^2+x+1)\\\\&amp;=(x^2+x+1)(x^4+x^3+x^2+x+1)\\end{split}$<\/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-9e71153 stk-block-background\" data-block-id=\"9e71153\"><style>.stk-9e71153{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-9e71153:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-9e71153-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-c41571b\" data-v=\"4\" data-block-id=\"c41571b\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-c41571b-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-c41571b-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-e756c12\" data-block-id=\"e756c12\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e09\uff1a\u56e0\u5f0f\u5206\u89e3$x^2-5x+1$\uff0c\u770b\u4f3c\u7b80\u5355\uff0c\u4f1a\u8005\u5be5\u5be5\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u8fd9\u662f\u4e00\u4e2a\u6807\u51c6\u7684\u4e8c\u6b21\u591a\u9879\u5f0f\uff0c\u53ef\u4ee5\u91c7\u7528\u901a\u7528\u7684\u914d\u65b9\u6cd5\u5206\u89e3\u56e0\u5f0f\u3002<br><br>$\\begin{split}\u89e3\uff1a\\\\&amp;\u539f\u5f0f=x^2-5x+\\left(\\frac{5}{2}\\right)^2-\\left(\\frac52\\right)^2+1\\\\&amp;=\\left(x-\\frac52\\right)^2-\\frac{21}{4}\\\\&amp;=\\left(x-\\frac52\\right)^2-\\left(\\frac{\\sqrt{21}}{2}\\right)^2\\\\&amp;=\\left(x-\\frac52+\\frac{\\sqrt{21}}{2}\\right)\\left(x-\\frac52-\\frac{\\sqrt{21}}{2}\\right)\\\\&amp;=\\left(x-\\frac{5-\\sqrt{21}}{2}\\right)\\left(x-\\frac{5+\\sqrt{21}}{2}\\right)\\end{split}$<\/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-f45a318 stk-block-background\" data-block-id=\"f45a318\"><style>.stk-f45a318{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-f45a318:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-f45a318-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-6190e0d\" data-v=\"4\" data-block-id=\"6190e0d\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-6190e0d-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-6190e0d-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-6598a0a\" data-block-id=\"6598a0a\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u56db\uff1a\u56e0\u5f0f\u5206\u89e3$x^{222}-1$\uff0c90%\u7684\u540c\u5b66\u5206\u89e3\u4e0d\u5f7b\u5e95\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u91c7\u7528\u5e73\u65b9\u5dee\u3001\u7acb\u65b9\u5dee\u516c\u5f0f\u5206\u89e3\u662f\u591a\u6570\u540c\u5b66\u7684\u601d\u8def\uff0c\u4f46\u662f90%\u7684\u540c\u5b66\u5206\u89e3\u5f97\u4e0d\u5f7b\u5e95\uff0c\u5173\u952e\u662f\u5bf9\u4e8e$\\displaystyle x^5-1=(x^4+x^3+x^2+x+1)$\u8fd9\u79cd\u7c7b\u4f3c\u7684\u516c\u5f0f\u53ef\u4ee5\u62d3\u5c55\u5230$x^n-1=(x-1)(x^{n-1}+x^{n-2}+\\cdots+x+1)$<br><br>$\\begin{split}\u89e3\uff1a\\\\&amp;\u539f\u5f0f=\\left(x^{111}\\right)^2-1^2\\\\&amp;=\\left(x^{111}+1\\right)\\left(x^{111}-1\\right)\\\\&amp;=\\left[\\left(x^{37}\\right)^3+1\\right]\\left[\\left(x^{37}\\right)^3-1\\right]\\\\&amp;=\\left(x^{37}+1\\right)\\left(x^{74}-x^{37}+1\\right)\\left(x^{37}-1\\right)\\left(x^{74}+x^{37}+1\\right)\\\\&amp;=\\left(x-1\\right)\\left(x^{36}+x^{35}+\\cdots+x+1\\right)\\left(x^{37}+1\\right)\\left(x^{74}-x^{37}+1\\right)\\left(x^{74}+x^{37}+1\\right)\\end{split}$<\/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-a92886e stk-block-background\" data-block-id=\"a92886e\"><style>.stk-a92886e{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-a92886e:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-a92886e-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-b593b42\" data-v=\"4\" data-block-id=\"b593b42\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-b593b42-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-b593b42-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-1a13d92\" data-block-id=\"1a13d92\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e94\uff1a\u56e0\u5f0f\u5206\u89e3$m^5n-9mn^5$\uff0c1980\u5e74\u7684\u9ad8\u8003\u9898\uff0c\u8fd9\u9898\u4e0d\u5f97\u5206\uff0c\u8003\u5927\u5b66\u6709\u96be\u5ea6\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u8fd8\u662f\u8bbe\u6cd5\u4f7f\u7528\u5e73\u65b9\u5dee\u3001\u7acb\u65b9\u5dee\u516c\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002<br><br>$\\begin{split}\u89e3\uff1a\\\\&amp;=mn\\left(m^4-9n^4\\right)\\\\&amp;=mn\\left[\\left(m^2\\right)^2-\\left(3n^2\\right)^2\\right]\\\\&amp;=mn(m^2+3n^2)(m^2-3n^2)\\\\&amp;=mn(m^2+3n^2)\\left[m^2-(\\sqrt3n)^2\\right]\\\\&amp;=mn\\left(m^2+3n^2\\right)\\left(m+\\sqrt3n\\right)\\left(m-\\sqrt3n\\right)\\end{split}$<\/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-f674d71 stk-block-background\" data-block-id=\"f674d71\"><style>.stk-f674d71{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-f674d71:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-f674d71-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-467f257\" data-v=\"4\" data-block-id=\"467f257\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-467f257-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-467f257-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-ce07190\" data-block-id=\"ce07190\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u516d\uff1a\u56e0\u5f0f\u5206\u89e3$x^4-4x^2+36$\uff0c\u770b\u4f3c\u7b80\u5355\uff0c\u96be\u5012\u4e0d\u5c11\u5b66\u751f\u4e0e\u5bb6\u957f\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u4e4d\u4e00\u770b\uff0c\u53ef\u4ee5\u628a\u524d\u4e24\u9879\u7ec4\u5408\u6210\u4e00\u4e2a\u5b8c\u5168\u5e73\u65b9\u5f0f\uff0c\u4f46\u662f\u7ec4\u5408\u540e\u53d1\u73b0\u65e0\u6cd5\u7ee7\u7eed\u5206\u89e3\u4e86\u3002\u8fd9\u9053\u9898\u76ee\u7684\u5de7\u5999\u4e4b\u5904\u5728\u4e8e\u89c2\u5bdf$36=6^2$\uff0c\u53ef\u4ee5\u8003\u8651\u589e\u51cf\u4e00\u4e2a\u4e8c\u6b21\u9879\u8fdb\u884c\u5206\u89e3\u3002<br><br>$\\begin{split}\u89e3\uff1a\\\\&amp;\u539f\u5f0f=\\left(x^2\\right)^2+12x^2+6^2-12x^2-4x^2\\\\&amp;=(x^2+6)^2-16x^2\\\\&amp;=(x^2+6)^2-(4x)^2\\\\&amp;=(x^2+6+4x)(x^2+6-4x)\\\\&amp;=(x^2+4x+6)(x^2-4x+6)\\end{split}$<\/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-81db75e stk-block-background\" data-block-id=\"81db75e\"><style>.stk-81db75e{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-81db75e:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-81db75e-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-9df77a3\" data-v=\"4\" data-block-id=\"9df77a3\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-9df77a3-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-9df77a3-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-470fc65\" data-block-id=\"470fc65\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e03\uff1a\u56e0\u5f0f\u5206\u89e3 $(a-b)^2(ab-2)-4$<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u5982\u679c\u5c55\u5f00\u4e8c\u6b21\u5f0f\u5219\u66f4\u590d\u6742\uff0c\u53ea\u80fd\u53e6\u8f9f\u8e4a\u5f84\u4e86\uff0c\u901a\u8fc7\u89c2\u5bdf\u53ef\u4ee5\u5c06$(a-b)^2$\u770b\u6210\u4e00\u4e2a\u6574\u4f53\uff0c\u901a\u8fc7\u53d8\u6362\u5148\u62c6\u5f00\u518d\u7ec4\u5408\uff0c\u8fdb\u800c\u5206\u89e3\u56e0\u5f0f\u3002<br><br>$\\begin{split}\\text{\u89e3\uff1a}\\\\&amp;\\text{\u539f\u5f0f=}ab(a-b)^2-2(a-b)^2-4\\\\&amp;=a(a-b)b(a-b)-2(a-b)(a-b)-4\\\\&amp;\\text{\u53ef\u4ee5\u5c06$a-b$\u770b\u4f5c\u6574\u4f53\u4f7f\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\uff1a}\\\\&amp;\\bbox[yellow,9pt,border:2px solid red]{\\begin{cases}a(a-b)\\qquad\\qquad+2\\\\b(a-b)\\qquad\\qquad-2\\end{cases}}\\\\&amp;\\text{\u6700\u7ec8\u7ed3\u679c\u539f\u5f0f=}\\left[a(a-b)+2\\right]\\left[b(a-b)-2\\right]\\end{split}$<\/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$x^{10}+x^2+1$\uff0c\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u9898\uff0c\u6709\u96be\u5ea6\u3002\u2003\u2003\u89e3\u9898\u601d\u8def\uff1a\u9ad8\u6b21\u9879\u662f10\uff0c\u4e00\u822c\u6765\u8bf4 [&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-621","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\/621","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=621"}],"version-history":[{"count":0,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=\/wp\/v2\/posts\/621\/revisions"}],"wp:attachment":[{"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=621"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=621"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=621"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}