{"id":2072,"date":"2024-08-15T07:49:02","date_gmt":"2024-08-14T23:49:02","guid":{"rendered":"http:\/\/www.jiaohuweike.online\/?p=2072"},"modified":"2026-03-03T11:04:09","modified_gmt":"2026-03-03T03:04:09","slug":"hsyldwt-5-4-2-2","status":"publish","type":"post","link":"http:\/\/jhwk.online\/?p=2072","title":{"rendered":"\u4e0d\u7b49\u5f0f\u3001\u57fa\u672c\u4e0d\u7b49\u5f0f"},"content":{"rendered":"\n\n\n\n\n\n\n\n<div class=\"wp-block-stackable-spacer stk-block-spacer stk--no-padding stk-block stk-711932c\" data-block-id=\"711932c\"><\/div>\n\n\n\n<div class=\"wp-block-ht-block-toc  is-style-outline htoc htoc--position-wide toc-list-style-plain\" data-htoc-state=\"expanded\"><span class=\"htoc__title\"><span class=\"ht_toc_title\">\u5185\u5bb9\u76ee\u5f55<\/span><span class=\"htoc__toggle\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16\" height=\"16\"><g fill=\"#444\"><path d=\"M15 7H1c-.6 0-1 .4-1 1s.4 1 1 1h14c.6 0 1-.4 1-1s-.4-1-1-1z\"><\/path><path d=\"M15 1H1c-.6 0-1 .4-1 1s.4 1 1 1h14c.6 0 1-.4 1-1s-.4-1-1-1zM15 13H1c-.6 0-1 .4-1 1s.4 1 1 1h14c.6 0 1-.4 1-1s-.4-1-1-1z\"><\/path><\/g><\/svg><\/span><\/span><div class=\"htoc__itemswrap\"><ul class=\"ht_toc_list\"><li class=\"\"><a href=\"\/#htoc-\">\u4e0d\u7b49\u5f0f\u7684\u6027\u8d28<\/a><\/li><li class=\"\"><a href=\"\/#htoc-111\">\u4e00\u5143\u4e8c\u6b21\u4e0d\u7b49\u5f0f<\/a><\/li><li class=\"\"><a href=\"\/#htoc-11111111111\">\u5206\u5f0f\u4e0d\u7b49\u5f0f<\/a><\/li><li class=\"\"><a href=\"\/#htoc-1111111111111\">\u57fa\u672c\u4e0d\u7b49\u5f0f<\/a><\/li><\/ul><\/div><\/div>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"htoc-\">\u4e0d\u7b49\u5f0f\u7684\u6027\u8d28<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1.\u5df2\u77e5\u5b9e\u6570  a, b, c  \u6ee1\u8db3  a&gt;b&gt;c , \u4e14  a+b+c=0 , \u5219\u4e0b\u5217\u8bf4\u6cd5\u6b63\u786e\u7684\u662f  ( ~~~~~~ )~~~~~~~~~~~~~~~~~~~~\\\\\nA\\frac{1}{a-c}&gt;\\frac{1}{b-c}~~~~\nB.  a-c&gt;2 b ~~~~\nC.  a^{2}&gt;b^{2} ~~~~\nD.  a b+b c&gt;0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-bc-b-a-b-gt-b-c-a-b-gt-a-2a-gt-b\"><pre>\u7b54\u6848\uff1aBC\uff1b\u63d0\u793a\uff1a\u9009\u9879B,\u53ea\u9700\u8bc1a-b&gt;b+c,\u5373a-b&gt;-a,\u53732a&gt;b,\u663e\u7136\u6210\u7acb.~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>2.\u5df2\u77e5\u5b9e\u6570  a, b, c  \u6ee1\u8db3  a&gt;b&gt;c , \u4e14  a+b+c=0 , \u6c42\\frac{c}{a}\u7684\u53d6\u503c\u8303\u56f4.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-11\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-2-frac-1-2-a-gt-0-b-a-c-a-gt-a-c-gt-c-a-rightarrow-1-gt-1-frac-c-a-gt-frac-c-a\"><pre>\u7b54\u6848\uff1a(-2,-\\frac{1}{2});~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\u63d0\u793a\uff1aa&gt;0,b=-(a+c)\u53ef\u5f97a&gt;-(a+c)&gt;c,\u540c\u9664\u4ee5a,\\Rightarrow 1&gt;-(1+\\frac{c}{a})&gt;\\frac{c}{a}~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"htoc-111\">\u4e00\u5143\u4e8c\u6b21\u4e0d\u7b49\u5f0f<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1.\u89e3\u4e0d\u7b49\u5f0f:\n\uff081\uff092x^2-3x-2&gt;0;(2)-6x^2-x+2\\ge 0;(3)x^2-3x&gt;0;(4)x^2&lt;9.~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-1-infty-frac-1-2-cup-2-infty-2-left-frac-2-3-frac-1-2-right-3-infty-0-cup-3-infty-4-3-3\"><pre>\u7b54\u6848\uff1a(1)(-\\infty ,-\\frac{1}{2} )\\cup (2,+\\infty );(2)\\left [ -\\frac{2}{3} ,\\frac{1}{2}  \\right ] ;(3)(-\\infty ,0 )\\cup (3,+\\infty );(4)(-3,3)~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>2.\u4e0d\u7b49\u5f0fax^2+ax-1&lt;0\u5bf9\\forall x \\in R\u6052\u6210\u7acb\uff0c\u6c42\u5b9e\u6570a\u7684\u53d6\u503c\u8303\u56f4.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-11111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-4-lt-a-le-0\"><pre>\u7b54\u6848\uff1a-4&lt; a\\le 0;\u63d0\u793a\uff1aa=0\u6216\\left\\{\\begin{matrix}\n a&lt;0 &amp; \\\\\n \\bigtriangleup &lt;0 &amp;\n\\end{matrix}\\right.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>3.\u5173\u4e8ex \u7684\u4e0d\u7b49\u5f0fx^2-4x-2-a\\le 0\u5728\u5b9e\u6570\u96c6R\u4e0a\u6709\u89e3,\u6c42\u5b9e\u6570a \u7684\u53d6\u503c\u8303\u56f4.~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-a-ge-6\"><pre>\u7b54\u6848\uff1aa\\ge -6\uff1b\u63d0\u793a\uff1a\\bigtriangleup\\ge0 .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>4.\u5173\u4e8ex \u7684\u4e0d\u7b49\u5f0fx^2-4x-2-a\\le 0\u5728x \\in [0,1]\u4e0a\u6709\u89e3,\u6c42\u5b9e\u6570a \u7684\u53d6\u503c\u8303\u56f4.~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-5-infty-a-ge-x-2-4x-2-x-in-0-1\"><pre>\u7b54\u6848\uff1a[-5,+\\infty);\u63d0\u793a\uff1a\u5206\u79bb\u53c2\u6570,a \\ge x^2-4x-2\u5728x \\in [0,1]\u4e0a\u6709\u89e3.~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>5.\u8bbe\u51fd\u6570  f(x)=m x^{2}-m x-1 , \u547d\u9898 \"  \\exists x \\in[1,3], f(x) \\leqslant-m+2  \" \u662f\u5047\u547d\u9898, \u6c42\u5b9e\u6570  m ~\\\\ \u7684\u53d6\u503c\u8303\u56f4.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-11111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-3-infty-m-gt-frac-3-x-2-x-1-forall-x-in-1-3-f-x-gt-m-2-mx-2-mx-m-3-gt-0-x-frac-1-2\"><pre>\u7b54\u6848\uff1a(3,+\\infty).\u63d0\u793a\uff1a\u6cd5\u4e00\u3001\u5206\u79bb\u53c2\u91cfm&gt;\\frac{3}{x^2-x+1};\u6cd5\u4e8c\u3001\u8f6c\u5316\u4e3a\"  \\forall x \\in[1,3], ~~~~~~~\\\\f(x) &gt;-m+2  \" \u662f\u771f\u547d\u9898\uff0c\u5373mx^2-mx+m-3&gt;0,\u8ba8\u8bba\u56fe\u8c61\uff0c\u6ce8\u610f\u6b64\u51fd\u6570\u7684\u5bf9~~~~~\\\\\u79f0\u8f74\u4e3a\u5b9a\u76f4\u7ebfx=\\frac{1}{2}.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>6.\u51fd\u6570f(x)=x^2+ax+3,\u5f53x \\in [-2,2]\u65f6\uff0cf(x)\\ge a\u6052\u6210\u7acb\uff0c\u6c42\u5b9e\u6570a\u7684\u8303\u56f4.~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-7-2-a-g-x-x-2-ax-3-a\"><pre>\u7b54\u6848\uff1a[-7,2];\u63d0\u793a\uff1a\u6cd5\u4e00\u3001\u5206\u79bb\u53c2\u91cfa,(x-1)a\\ge -x^2-3,\u8ba8\u8bbax\\in [-2,1),x=1,~~~~~\\\\x\\in(1,2]\u4e09\u79cd\u60c5\u51b5\uff1b\u6cd5\u4e8c\u3001\u4e0d\u5206\u79bb\u53c2\u6570a,\u76f4\u63a5\u8ba8\u8bbag(x)=x^2+ax+3-a\u7684\u5bf9\u79f0\u8f74~~~~~\\\\x=-\\frac{a}{2} \\le-2,-\\frac{a}{2}\\in(-2,2),-\\frac{a}{2} \\ge2\u4e09\u79cd\u60c5\u51b5.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>7.\u82e5\u4e0d\u7b49\u5f0f  x^{2}+p x&gt;4 x+p-3 , \u5f53  0 \\leqslant p \\leqslant 4  \u65f6\u6052\u6210\u7acb, \u6c42  x  \u7684\u53d6\u503c\u8303\u56f4.~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-infty-1-cup-3-infty-p-f-p-x-1-p-x-2-4x-3-left-begin-matrix-f-0-gt-0-f-4-gt-0-end-matrix-right\"><pre>\u7b54\u6848\uff1a(-\\infty,-1)\\cup (3,+\\infty).\u63d0\u793a\uff1a\u8f6c\u5316\u4e3a\u5173\u4e8ep\u7684\u4e00\u6b21\u51fd\u6570~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\f(p)=(x-1)p+x^2-4x+3,\u53ea\u9700\\left\\{\\begin{matrix}\nf(0)&gt;0 \\\\f(4)&gt;0\n\n\\end{matrix}\\right..~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"htoc-11111111111\">\u5206\u5f0f\u4e0d\u7b49\u5f0f<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\u4e24\u79cd\u6a21\u578b<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1.\\frac{f(x)}{g(x)}&gt;0\\Leftrightarrow  f(x)g(x)&gt;0;~~~~~~~~~2.\\frac{f(x)}{g(x)}\\ge 0\\Leftrightarrow  \\left\\{\\begin{matrix}\n f(x)g(x)\\ge 0 &amp; \\\\\n  g(x)\\ne 0&amp;\n\\end{matrix}\\right.\n<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div style=\"height:30px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>1.\u89e3\u4e0b\u5217\u5206\u5f0f\u4e0d\u7b49\u5f0f:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(1)  \\frac{2 x-5}{x+1}&gt;0  \uff1b\n(2)  \\frac{3 x-1}{2-x} \\geq 0 ;\n(3)  \\frac{3 x-1}{2-x} \\leq 1 ;\n(4)  \\frac{x^{2}-3 x+2}{x^{2}-2 x-3}&lt;0 .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(5)  \\frac{1}{x+1}&lt;\\frac{1}{x}+1 ;\n(6)  \\frac{2 x^{2}-7 x+3}{x^{2}-4 x+4} \\geq 2 .~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-1-infty-1-cup-left-frac-5-2-infty-right-2-left-frac-1-3-2-right-3-left-infty-frac-3-4-right-cup-2-infty-4-1-1-cup-2-3-5-infty-1-cup-0-infty-6-5-infty\"><pre> (1)(-\\infty,-1) \\cup\\left(\\frac{5}{2},+\\infty\\right) ;\n(2)  \\left[\\frac{1}{3}, 2\\right) ;\n(3)  \\left(-\\infty, \\frac{3}{4}\\right] \\cup(2,+\\infty) ;\n(4)  (-1,1) \\cup(2,3) ;~~~~~~~\\\\\n\n(5)  (-1,0);\n(6)  [5,+\\infty) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"htoc-1111111111111\">\u57fa\u672c\u4e0d\u7b49\u5f0f<\/h4>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre> 1.\u5df2\u77e5y=x+\\frac{1}{x}\uff0c\u6839\u636e\u6761\u4ef6\u6c42\u503c\u3002~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\(1)x&gt;0\uff0c\u6c42y\u7684\u6700\u5c0f\u503c;(2)x\\ge \\frac{1}{2}\uff0c\u6c42y\u7684\u6700\u5c0f\u503c;(3)x\\ge 2\uff0c\u6c42y\u7684\u6700\u5c0f\u503c;~~~~~~~~~~~~~~~~~~~~\\\\(4)x&lt;0\uff0c\u6c42y\u7684\u6700\u5927\u503c;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-11111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-1-2-2-2-3-frac-5-2-4-2\"><pre>(1)2;(2)2;(3)\\frac{5}{2};(4)-2.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>2.(1)\u5df2\u77e5  x&gt;-1, \u6c42x+\\frac{1}{x+1}  \u7684\u6700\u5c0f\u503c;\n(2) \u5df2\u77e5  x&gt;-1,\u6c422x+\\frac{1}{x+1}  \u7684\u6700\u5c0f\u503c.~~~~~~~~~\\\\\n<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(3) \u5df2\u77e5  x&gt;1,\u6c422 x+\\frac{4}{x-1}  \u7684\u6700\u5c0f\u503c; (4)\u5df2\u77e50 &lt; x &lt; \\frac{1}{2}, \u6c42\\sqrt{x(1-2 x)}  \u7684\u6700\u5927\u503c.~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(5)\u6c42\\sqrt{x^2+4}+\\frac{1}{\\sqrt{x^2+4}}\u7684\u6700\u5c0f\u503c;(6)\u6c42\\frac{x^2+2}{\\sqrt{x^2+1}}\u7684\u6700\u5c0f\u503c.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-1-1-2-2-sqrt-2-2-3-4-sqrt-2-2-4-frac-sqrt-2-4-5-frac-5-2-6-2\"><pre>(1)1;(2)2\\sqrt{2}-2;(3)4\\sqrt{2}+2;(4)\\frac{\\sqrt{2}}{4};(5)\\frac{5}{2};(6)2.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>3.(1) \u5df2\u77e5  a, b&gt;0, a+b=2 ,\u6c42 \\frac{1}{a}+\\frac{2}{b}  \u7684\u6700\u5c0f\u503c;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(2)\u5df2\u77e5  a, b&gt;0, a+b=2 , \u6c42\\frac{1}{a}+\\frac{2 a}{b} \u7684\u6700\u5c0f\u503c;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(3)\u5df2\u77e5  a, b&gt;0, a+b=2 ,\u6c42  \\frac{2 a+3}{a+1}+\\frac{1}{b}  \u7684\u6700\u5c0f\u503c;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(4)\u5df2\u77e5  x, y&gt;0 , \u4e14 x+y=2 , \u6c42  \\frac{2}{x+3 y}+\\frac{1}{x-y}  \u7684\u6700\u5c0f\u503c;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>(5)\u5df2\u77e5-1 &lt; a&lt; 2,\u6c42\\frac{1}{1+a}+\\frac{4}{2-a}\u7684\u6700\u5c0f\u503c.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-1111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-1-sqrt-2-frac-3-2-2-frac-5-2-3-frac-10-3-4-frac-2-sqrt-2-3-4-5-3\"><pre>\u7b54\u6848\uff1a(1)\\sqrt{2}+\\frac{3}{2};(2)\\frac{5}{2};(3)\\frac{10}{3};(4)\\frac{2\\sqrt{2} +3}{4} ;(5)3.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>4.\u5df2\u77e5x&gt;0\uff0cy\\ge 0\uff0c\u4e14x\uff0b2y\uff1d1,\u6c42\\frac{x+2y+1}{x}-\\frac{4}{x+y}\u7684\u6700\u5c0f\u503c.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-11111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-2-frac-x-2-y-1-x-frac-4-x-y-frac-x-2-y-x-2-y-x-frac-4-x-8-y-x-y-frac-4-x-4-y-2-x-x-frac-8-x-8-y-4-x-x-y-frac-4-x-4-y-x-frac-4-x-x-y-10-geqslant-2-sqrt-frac-4-x-4-y-x-cdot-frac-4-x-x-y-10-2\"><pre> \u7b54\u6848\uff1a-2\uff1b\u63d0\u793a\uff1a\\frac{x+2 y+1}{x}-\\frac{4}{x+y}=\\frac{x+2 y+x+2 y}{x}-\\frac{4 x+8 y}{x+y} ~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\=\\frac{4 x+4 y-2 x}{x}-\\frac{8 x+8 y-4 x}{x+y}=\\frac{4 x+4 y}{x}+\\frac{4 x}{x+y}-10\\geqslant 2 \\sqrt{\\frac{4 x+4 y}{x} \\cdot \\frac{4 x}{x+y}}-10\\\\=-2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>5.(1)\u5df2\u77e5  x&gt;0, y&gt;0, x+3 y+x y=9  \uff0c\u6c42  x+3 y  \u7684\u6700\u5c0f\u503c\uff1b~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n\\\\(2)\u82e5\u6b63\u6570  x, y  \u6ee1\u8db3  x^{2}-x y+2=0 ,\u6c42  x+y  \u7684\u6700\u5c0f\u503c;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\\\\n(3)\u82e5  x, y  \u4e3a\u6b63\u5b9e\u6570, \u82e5  x+2 y=3 x y ,\u6c42 2 x+y  \u7684\u6700\u5c0f\u503c.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<details class=\"wp-block-details is-layout-flow wp-block-details-is-layout-flow\"><summary>\u7b54\u6848<\/summary>\n<p id=\"htoc-111111111111111111\"><\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\" id=\"htoc-1-6-9-x-3y-xy-le-left-frac-x-3y-2-right-2-y-frac-9-x-3-x-x-3y-x-frac-27-3x-3-x-2-4-y-x-frac-2-x-3-3-xy-frac-1-y-frac-2-x-3\"><pre>(1)\u7b54\u6848\uff1a6\uff1b\u63d0\u793a\uff1a\u65b9\u6cd5\u4e00\uff1a\u57fa\u672c\u4e0d\u7b49\u5f0f9-(x+3y)=xy\\le \\left ( \\frac{x+3y}{2}  \\right ) ^2;\u65b9\u6cd5\u4e8c\uff1a~~~\\\\\u8f6c\u5316\u4e3a\u51fd\u6570,y=\\frac{9-x}{3+x},x+3y=x+\\frac{27-3x}{3+x};(2)\u7b54\u6848\uff1a4;\u63d0\u793a\uff1a\u8f6c\u5316\u4e3a\u51fd\u6570,~~~~~~~~~~~~~\\\\y=x+\\frac{2}{x};(3)\u7b54\u6848\uff1a3\uff1b\u63d0\u793a\uff1a\u540c\u9664\u4ee5xy\u5f97\\frac{1}{y}+\\frac{2}{x}=3.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<\/pre><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n<\/details>\n","protected":false},"excerpt":{"rendered":"<p>\u4e0d\u7b49\u5f0f\u7684\u6027\u8d28\u3001\u57fa\u672c\u4e0d\u7b49\u5f0f\u7684\u5e94\u7528<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-2072","post","type-post","status-publish","format-standard","hentry","category-14"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/2072","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2072"}],"version-history":[{"count":4,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/2072\/revisions"}],"predecessor-version":[{"id":5784,"href":"http:\/\/jhwk.online\/index.php?rest_route=\/wp\/v2\/posts\/2072\/revisions\/5784"}],"wp:attachment":[{"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2072"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2072"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/jhwk.online\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2072"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}