{"id":549,"date":"2024-01-29T17:14:33","date_gmt":"2024-01-29T09:14:33","guid":{"rendered":"https:\/\/big-tan.top\/?p=549"},"modified":"2024-01-30T16:19:37","modified_gmt":"2024-01-30T08:19:37","slug":"%e4%bb%a3%e6%95%b0%e5%bc%8f%e6%b1%82%e5%80%bc%e9%97%ae%e9%a2%98%e6%8a%80%e5%b7%a7%e9%9b%86%e9%94%a6%ef%bc%88%e4%b8%80%ef%bc%89-2","status":"publish","type":"post","link":"https:\/\/itantan.eu.org\/?p=549","title":{"rendered":"\u521d\u4e2d\u6570\u5b66\u89e3\u65b9\u7a0b\u6280\u5de7\u96c6\u9526\uff08\u4e00\uff09"},"content":{"rendered":"\n<div class=\"wp-block-stackable-columns stk-block-columns stk-block stk-58bb5c6 stk-block-background\" data-block-id=\"58bb5c6\"><style>.stk-58bb5c6{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-58bb5c6:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-58bb5c6-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-15add15\" data-v=\"4\" data-block-id=\"15add15\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-15add15-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-15add15-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-6ae6644\" data-block-id=\"6ae6644\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e00\uff1a\u89e3\u65b9\u7a0b$(2x+7)(x^2-9)(2x-5)=91$\uff0c\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u8bd5\u9898\uff0c\u5de7\u89e3\u9ad8\u6b21\u65b9\u7a0b\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u4e4d\u4e00\u770b\uff0c\u60f3\u5230\u5c06\u65b9\u7a0b\u5de6\u8fb9\u5c55\u5f00\uff0c\u4f46\u662f\u518d\u4e00\u60f3\uff0c\u5de6\u8fb9\u5c55\u5f00\u540e\u6709$x^4\u3001x^3$\u9879\uff0c\u65e0\u6cd5\u4f7f\u7528\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u6c42\u6839\u516c\u5f0f\uff0c\u89e3\u9ad8\u6b21\u65b9\u7a0b\u96be\u5ea6\u6781\u5927\uff0c\u663e\u7136\u4e0d\u884c\u3002\u901a\u8fc7\u89c2\u5bdf\u53d1\u73b0\uff0c\u4e2d\u95f4\u9879\u662f\u5e73\u65b9\u5dee\uff0c\u611f\u89c9\u5e94\u8be5\u53ef\u4ee5\u901a\u8fc7\u5c55\u5f00\u5e73\u65b9\u5dee\u9879\uff0c\u7136\u540e\u9519\u4f4d\u76f8\u4e58\uff0c\u518d\u901a\u8fc7\u6362\u5143\u6cd5\u6c42\u89e3\u3002<br><br>$\\begin{split}\u89e3\uff1a\\\\&amp;\u539f\u5f0f=(2x+7)(x-3)(x+3)(2x-5)=91\\\\&amp;\\therefore(2x^2+x-21)(2x^2+x-15)=91\\\\&amp;\u901a\u8fc7\u89c2\u5bdf\u53d1\u73b0\uff0c\u5e38\u6570\u9879\u662f15\u4e0e21\uff0c\u53ef\u4ee5\u8003\u8651\u91c7\u7528\u5e73\u5747\u503c\u6362\u5143\u6cd5\u51d1\u6210\u5e73\u65b9\u5dee\u9879\uff1a\\\\&amp;\u4ee42x^2+x-18=t\\\\&amp;\\therefore\u539f\u5f0f\u6362\u5143\u540e\u53ef\u5f97\uff1a(t-3)(t+3)=91\\\\&amp;\\therefore t^2-9=91\\Rightarrow t^2=100\\Rightarrow t=\\pm10\\\\&amp;\u5206\u522b\u4ee3\u5165\u6362\u5143\u540e\u7684\u65b9\u7a0b\uff1a\\begin{cases}2x^2+x-18=10\\Rightarrow2x^2+x-28=0\\ldots(1)\\\\2x^2+x-18=-10\\Rightarrow2x^2+x-8=0\\ldots(2)\\end{cases}\\\\&amp;\\because \\Delta_1=1^2-4\\times2\\times(-28)=225\\gt0\\\\&amp;\\therefore x=\\frac{-1\\pm\\sqrt{1^2-4\\times2\\times(-28)}}{2\\times2}=\\frac{-1\\pm15}{4}\\\\&amp;\\therefore x_1=\\frac72\uff0cx_2=-4\\\\&amp;\\because\\Delta_2=1^2-4\\times2\\times(-8)=65\\gt0\\\\&amp;\\therefore x=\\frac{-1\\pm\\sqrt{1^2-4\\times2\\times(-8)}}{2\\times2}=\\frac{-1\\pm\\sqrt{65}}{4}\\\\&amp;\\therefore x_3=\\frac{-1+\\sqrt{65}}{4}\uff0cx_4=\\frac{-1-\\sqrt{65}}{4}\\\\&amp;\\therefore\u539f\u65b9\u7a0b\u5f0f\u6709\u56db\u4e2a\u6839\uff0c\u7c7b\u4f3c\u9ad8\u6b21\u65b9\u7a0b\u5747\u53ef\u901a\u8fc7\u8fd9\u79cd\u6362\u5143\u6cd5\u6c42\u89e3\u3002\\end{split}$<\/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-e368787 stk-block-background\" data-block-id=\"e368787\"><style>.stk-e368787{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-e368787:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-e368787-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-5686b1d\" data-v=\"4\" data-block-id=\"5686b1d\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-5686b1d-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-5686b1d-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-cec71db\" data-block-id=\"cec71db\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e8c\uff1a\u89e3\u65b9\u7a0b$\\displaystyle\\sqrt{x+16}+\\sqrt{x+51}=7$<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u5bf9\u4e8e\u7c7b\u4f3c \u6839\u5f0f\u65b9\u7a0b\uff0c\u901a\u5e38\u53ef\u4ee5\u91c7\u7528\u79fb\u9879\u540e\u4e24\u8fb9\u540c\u65f6\u5e73\u65b9\u53bb\u6839\u53f7\u7684\u65b9\u6cd5\u6c42\u89e3\uff1b\u4e5f\u53ef\u4ee5\u91c7\u7528\u6362\u5143\u6cd5\u6c42\u89e3\uff0c\u76f8\u5bf9\u800c\u8a00\uff0c\u6362\u5143\u6cd5\u66f4\u52a0\u7b80\u6d01\u3002<br><br>$\\begin{split}\u89e3\u6cd5\u4e00\uff1a\\\\&amp;\u79fb\u9879\uff1a\\sqrt{x+16}=7-\\sqrt{x+51}\\\\&amp;\u7b49\u5f0f\u4e24\u8fb9\u540c\u65f6\u5e73\u65b9\uff1a\\\\&amp;x+16=49+x+51-14\\sqrt{x+51}\\\\&amp;\u6574\u7406\u5f97\uff1a14\\sqrt{x+51}=84\\Rightarrow \\sqrt{x+51}=6\\\\&amp;\\therefore x+51=36\\\\&amp;\\therefore x=-15\\end{split}$<br><br>$\\begin{split}&amp;\u89e3\u6cd5\u4e8c\uff1a\u7528\u6362\u5143\u6cd5\u6c42\u89e3\u66f4\u7b80\u6d01\u3002\\\\&amp;\u4ee4\\sqrt{x+16}=a\uff0c\\sqrt{x+51}=b\\Rightarrow \\begin{cases}a^2=x+16\\\\b^2=x+51\\end{cases}\\\\&amp;\\therefore\\begin{cases}a+b=7\\\\a^2-b^2=(a+b)(a-b)=-35\\end{cases}\\\\&amp;\\therefore \\begin{cases}a+b=7\\ \\ \\ \\ldots(1)\\\\a-b=-5\\ldots(2)\\end{cases}\\\\&amp;\\therefore(1)+(2)\u53ef\u5f97\uff1a2a=2\\Rightarrow a=1\\\\&amp;\\therefore\\sqrt{x+16}=1\\\\&amp;\\therefore x=-15\\\\&amp;\u4ee3\u5165\u539f\u65b9\u7a0b\u9a8c\u7b97\u540e\u65e0\u8bef\u3002\\end{split}$<\/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-60a8b70 stk-block-background\" data-block-id=\"60a8b70\"><style>.stk-60a8b70{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-60a8b70:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-60a8b70-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-ddfb391\" data-v=\"4\" data-block-id=\"ddfb391\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-ddfb391-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-ddfb391-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-bfa297f\" data-block-id=\"bfa297f\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e09\uff1a\u89e3\u65b9\u7a0b$x^3=11x-20$\uff0c\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u9898\u76ee\uff0c\u8981\u6562\u4e8e\u5c1d\u8bd5\u65b0\u7684\u89e3\u6cd5\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u8fd9\u662f\u4e00\u4e2a\u9ad8\u6b21\u65b9\u7a0b\uff0c\u76f4\u63a5\u6c42\u89e3\u96be\u5ea6\u8f83\u5927\uff0c\u89c2\u5bdf\u53d1\u73b0\uff0c\u8be5\u65b9\u7a0b\u7f3a\u5c11\u4e8c\u6b21\u9879\uff0c\u53ef\u4ee5\u8bbe\u6cd5\u7ed9\u65b9\u7a0b\u4e24\u8fb9\u540c\u65f6\u52a0\u4e00\u4e2a\u4e8c\u6b21\u9879\uff0c\u4e24\u8fb9\u5206\u522b\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u7136\u540e\u518d\u79fb\u9879\u63d0\u53d6\u516c\u56e0\u5f0f\uff0c\u8fdb\u800c\u8fbe\u5230\u964d\u5e42\uff0c\u6700\u7ec8\u6c42\u89e3\u3002\u7c7b\u4f3c\u9898\u76ee\u7684\u57fa\u672c\u601d\u8def\u5c31\u662f\u5982\u6b64\u3002<br><br>\u89e3\uff1a<br>\u2003\u2003\u5173\u952e\u662f\u65b9\u7a0b\u4e24\u8fb9\u540c\u65f6\u52a0$ax^2$\u7684$a$\u7a76\u7adf\u5e94\u8be5\u662f\u591a\u5c11\uff1f\u901a\u8fc7\u5206\u6790\u65b9\u7a0b\u53f3\u8fb9\uff0c\u52a0$4x^2$\u6700\u6709\u53ef\u80fd\u3002<br>$\\begin{split}\\\\&amp;\u7b49\u5f0f\u4e24\u8fb9\u540c\u65f6\u52a04x^2\uff1a\\\\&amp;x^3+4x^2=4x^2+11x-20\\\\&amp;\\therefore x^2(x+4)=(x+4)(4x-5)\\\\&amp;\\because\u65e0\u6cd5\u5224\u65adx+4\u662f\u5426\u7b49\u4e8e0\uff0c\u6240\u4ee5\u4e0d\u80fd\u76f4\u63a5\u9664\u4ee5(x+4)\u964d\u5e42\uff0c\u53ea\u80fd\u79fb\u9879\u3002\\\\&amp;\\therefore x^2(x+4)-(x+4)(4x-5)\\\\&amp;\\therefore (x+4)(x^2-4x+5)=0\\\\&amp;\\therefore\\begin{cases}x+4=0\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ldots(1)\\\\x^2-4x+5=0\\ldots(2)\\end{cases}\\\\&amp;\\therefore (1)\\Rightarrow x=-4\\\\&amp;\\because(2)\u5f0f\u7684\\Delta=(-4)^2-4\\times1\\times5=-4\\lt0\\therefore(2)\u5f0f\u65e0\u5b9e\u6839\u3002\\\\&amp;\\therefore x=-4\\ \\ \\ \u662f\u6b64\u65b9\u7a0b\u552f\u4e00\u7684\u5b9e\u6839\u3002\\end{split}$<\/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-91c3544 stk-block-background\" data-block-id=\"91c3544\"><style>.stk-91c3544{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-91c3544:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-91c3544-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-79154b8\" data-v=\"4\" data-block-id=\"79154b8\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-79154b8-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-79154b8-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-f9767bd stk-block-background\" data-block-id=\"f9767bd\"><style>.stk-f9767bd{background-color:#ffe2c7 !important}.stk-f9767bd:before{background-color:#ffe2c7 !important}<\/style><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u56db\uff1a\u89e3\u65b9\u7a0b$\\displaystyle\\sqrt{x}+\\sqrt{x+5}+2\\sqrt{x^2+5x}=25-2x$<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u89c2\u5bdf\u53d1\u73b0$\\displaystyle2\\sqrt{x^2+5x}=2\\sqrt{x(x+5)}=2\\sqrt{x}\\sqrt{x+5}$\uff0c\u539f\u65b9\u7a0b\u53ef\u4ee5\u8bbe\u6cd5\u53d8\u6362\u6210\u4e3a\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u7684\u5f62\u5f0f\u8fdb\u884c\u6c42\u89e3\u3002<br><br>$\\begin{split}\u89e3\uff1a\\\\&amp;\u539f\u65b9\u7a0b\u53ef\u4ee5\u53d8\u5f62\u4e3a\uff1a\\\\&amp;2x+\\sqrt{x}+\\sqrt{x+5}+2\\sqrt{x}\\sqrt{x+5}-25=0\\\\&amp;\\therefore x+2\\sqrt{x}\\sqrt{x+5}+(x+5)+\\sqrt{x}+\\sqrt{x+5}-30=0\\\\&amp;\\therefore(\\sqrt{x}+\\sqrt{x+5})^2+(\\sqrt{x}+\\sqrt{x+5})-30=0\\\\&amp;\u5c06(\\sqrt{x}+\\sqrt{x+5})\u770b\u6210\u4e00\u4e2a\u6574\u4f53a\uff0c\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u53ef\u5f97\uff1a\\\\&amp;(\\sqrt{x}+\\sqrt{x+5}+6)(\\sqrt{x}+\\sqrt{x+5}-5)=0\\\\&amp;\\therefore\\sqrt{x}+\\sqrt{x+5}+6=0\\ldots(1)\u6216\u8005\\sqrt{x}+\\sqrt{x+5}-5=0\\ldots(2)\\\\&amp;\\because(1)\u5f0f\u4e2d\\sqrt{x}\\ge0\u4e14\\sqrt{x+5}\\ge0\\therefore(1)\\ge0\\Rightarrow(1)\u5f0f\u65e0\u5b9e\u6839\uff08\u820d\u53bb\uff09\u3002\\\\&amp;\\therefore\\sqrt{x}+\\sqrt{x+5}-5=0\\\\&amp;\\therefore\\sqrt{x}=5-\\sqrt{x+5}\\\\&amp;\\therefore x=25-10\\sqrt{x+5}+x+5\\\\&amp;\\therefore10\\sqrt{x+5}=30\\\\&amp;\\therefore\\sqrt{x+5}=3\\\\&amp;\\therefore x+5=9\\Rightarrow x=4\\\\&amp;\u4ee3\u5165\u539f\u65b9\u7a0b\u68c0\u9a8c\u540e\u6b63\u786e\u65e0\u8bef\uff0cx=4\u662f\u539f\u65b9\u7a0b\u7684\u5b9e\u6839\u3002\\end{split}$<\/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-c5926cb stk-block-background\" data-block-id=\"c5926cb\"><style>.stk-c5926cb{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-c5926cb:before{background-color:#F6F6F6 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-c5926cb-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-b0ead0f\" data-v=\"4\" data-block-id=\"b0ead0f\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-b0ead0f-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-b0ead0f-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-eedf4c8 stk-block-background\" data-block-id=\"eedf4c8\"><style>.stk-eedf4c8{background-color:#F6F6F6 !important}.stk-eedf4c8:before{background-color:#F6F6F6 !important}<\/style><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u4e94\uff1a\u89e3\u65b9\u7a0b$\\displaystyle\\frac{x-2}{2016}+\\frac{x}{2017}+\\frac{x+2}{2018}=6$<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u4e4d\u4e00\u770b\uff0c\u8fd9\u5c31\u662f\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\uff0c\u53ef\u4ee5\u901a\u5206\u540e\u6c42\u89e3\uff0c\u4f46\u662f\u7531\u4e8e\u5206\u6bcd\u8f83\u5927\uff0c\u901a\u5206\u7684\u8ba1\u7b97\u91cf\u8f83\u5927\u3002\u7c7b\u4f3c\u9898\u76ee\uff0c\u4e00\u5b9a\u6709\u7b80\u4fbf\u65b9\u6cd5\uff0c\u901a\u8fc7\u89c2\u5bdf\u53d1\u73b0\uff0c\u65b9\u7a0b\u53f3\u8fb9\u662f$\\displaystyle6=2+2+2=\\frac{4032}{2016}+\\frac{4034}{2017}+\\frac{4036}{2018}$\uff0c\u800c\u5de6\u8fb9\u4e09\u4e2a\u5206\u6570\u7684\u5206\u5b50\u5206\u522b\u76f8\u5dee2\uff0c\u80fd\u5426\u5c066\u79fb\u9879\u540e\u5206\u5288\u6210\u4e09\u4e2a2\uff0c\u7136\u540e\u5206\u522b\u76f8\u51cf\u6c42\u89e3\u5462\uff1f<br><br>$\\begin{split}\u89e3\uff1a\\\\&amp;\u539f\u65b9\u7a0b\u53ef\u4ee5\u53d8\u5f62\u4e3a\uff1a\\\\&amp;\\left(\\frac{x-2}{2016}-2\\right)+\\left(\\frac{x}{2017}-2\\right)+\\left(\\frac{x+2}{2018}-2\\right)=0\\\\&amp;\\therefore\\frac{x-2-4032}{2016}+\\frac{x-4034}{2017}+\\frac{x+2-4036}{2018}=0\\\\&amp;\\therefore(x-4034)(\\frac1{2016}+\\frac1{2017}+\\frac1{2018})=0\\\\&amp;\\because\\frac1{2016}+\\frac1{2017}+\\frac1{2018}\\gt0\\\\&amp;\\therefore x-4034=0\\\\&amp;\\therefore x=4034\\ \\ \u4e0d\u7528\u901a\u5206\uff0c\u76f4\u63a5\u6c42\u89e3\uff0c30\u79d2\u949f\u8db3\u591f\u3002\\end{split}$<\/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-b600f1c stk-block-background\" data-block-id=\"b600f1c\"><style>.stk-b600f1c{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-b600f1c:before{background-color:#ffe2c7 !important}<\/style><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-b600f1c-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-7c5b434\" data-v=\"4\" data-block-id=\"7c5b434\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-7c5b434-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-7c5b434-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-0871148\" data-block-id=\"0871148\"><p class=\"stk-block-text__text\">\u2003\u2003<strong>\u9898\u76ee\u516d\uff1a\u89e3\u65b9\u7a0b$\\displaystyle x^2+\\frac{16x^2}{(x-4)^2}=180$\uff0c\u5fb7\u56fd\u4e2d\u5b66\u6570\u5b66\u7ade\u8d5b\u9898\uff0c\u6ca1\u6709\u786c\u529f\u592b\u4e00\u65f6\u534a\u4f1a\u89e3\u4e0d\u51fa\u6765\u3002<\/strong><br>\u2003\u2003<strong>\u89e3\u9898\u601d\u8def\uff1a<\/strong>\u8fd9\u662f\u4e00\u4e2a\u5206\u5f0f\u65b9\u7a0b\uff0c\u901a\u5e38\u6765\u8bf4\u5206\u5f0f\u65b9\u7a0b\u9700\u8981\u8f6c\u5316\u4e3a\u6574\u5f0f\u65b9\u7a0b\u6c42\u89e3\uff0c\u4f46\u662f\u8fd9\u4e2a\u65b9\u7a0b\u7684\u5206\u5b50\u542b\u6709\u4e8c\u6b21\u9879\uff0c\u8f6c\u5316\u4e3a\u6574\u5f0f\u65b9\u7a0b\u540e\u662f\u56db\u6b21\u65b9\u7a0b\uff0c\u65e0\u6cd5\u76f4\u63a5\u6c42\u89e3\uff0c\u56e0\u6b64\uff0c\u9700\u8981\u53e6\u8f9f\u8e4a\u5f84\uff0c\u8fd9\u79cd\u9ad8\u6b21\u65b9\u7a0b\u4e00\u822c\u7684\u601d\u8def\u662f\uff0c\u901a\u8fc7\u8f6c\u6362\u4ee5\u53ca\u6362\u5143\u5c06\u539f\u65b9\u7a0b\u964d\u5e42\uff0c\u7136\u540e\u5206\u6b65\u6c42\u89e3\u3002<br><br>$\\begin{split}\u89e3\uff1a\\\\&amp;\u539f\u65b9\u7a0b\u53ef\u4ee5\u8fdb\u884c\u53d8\u5f62\uff1a\\\\&amp;x^2+\\left(\\frac{4x}{x-4}\\right)^2=180\\\\&amp;\\therefore x^2+2x\\frac{4x}{x-4}+\\left(\\frac{4x}{x-4}\\right)^2=180+2x\\frac{4x}{x-4}\\\\&amp;\\therefore \\left(x+\\frac{4x}{x-4}\\right)^2=180+\\frac{8x^2}{x-4}\\\\&amp;\\therefore \\left(\\frac{x^2}{x-4}\\right)^2=180+\\frac{8x^2}{x-4}\\\\&amp;\u4ee4\\frac{x^2}{x-4}=a\\\\&amp;\u5219\u6709\uff1aa^2=180+8a\\\\&amp;\\therefore a^2-8a-180=0\\\\&amp;\\therefore (a-18)(a+10)=0\\\\&amp;\\therefore a=18\u6216\u8005a=-10\\\\&amp;\u4ee3\u5165\u6362\u5143\u5f0f\u6709\uff1a\\frac{x^2}{x-4}=18\u6216\\frac{x^2}{x-4}=-10\\\\&amp;\u6574\u7406\u5f97\uff1ax^2-18x+72=0\\ldots(1)\u6216x^2+10x-40=0\\ldots(2)\\\\&amp;(1)\u5f0f\\Rightarrow (x-12)(x-6)=0\\\\&amp;x_1=12\uff0cx_2=6\\\\&amp;(2)\u5f0f\\Rightarrow x_{3,4}=\\frac{-10\\pm\\sqrt{100-4\\times1\\times(-40)}}{2}=-5\\pm\\sqrt{65}\\end{split}$<\/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-6d952ad\" data-block-id=\"6d952ad\"><div class=\"stk-row stk-inner-blocks stk-block-content stk-content-align stk-6d952ad-column\">\n<div class=\"wp-block-stackable-column stk-block-column stk-column stk-block stk-777e812\" data-v=\"4\" data-block-id=\"777e812\"><div class=\"stk-column-wrapper stk-block-column__content stk-container stk-777e812-container stk--no-background stk--no-padding\"><div class=\"stk-block-content stk-inner-blocks stk-777e812-inner-blocks\">\n<div class=\"wp-block-stackable-text stk-block-text stk-block stk-537697f\" data-block-id=\"537697f\"><p class=\"stk-block-text__text\"><\/p><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u2003\u2003\u9898\u76ee\u4e00\uff1a\u89e3\u65b9\u7a0b$(2x+7)(x^2-9)(2x-5)=91$\uff0c\u521d\u4e2d\u6570\u5b66\u7ade\u8d5b\u8bd5\u9898\uff0c\u5de7\u89e3\u9ad8\u6b21\u65b9\u7a0b\u3002\u2003\u2003\u89e3\u9898\u601d [&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-549","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\/549","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=549"}],"version-history":[{"count":0,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=\/wp\/v2\/posts\/549\/revisions"}],"wp:attachment":[{"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=549"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=549"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/itantan.eu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=549"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}