{"id":7305,"date":"2023-11-27T21:32:40","date_gmt":"2023-11-27T13:32:40","guid":{"rendered":"http:\/\/www.aiersheng.cc\/?p=7305"},"modified":"2024-01-02T16:52:07","modified_gmt":"2024-01-02T08:52:07","slug":"7305","status":"publish","type":"post","link":"https:\/\/www.aiersheng.cc\/?p=7305","title":{"rendered":"\u4e13\u5347\u672c\u6570\u5b66\u8003\u8bd5\u901a\u5e38\u5305\u62ec\u57fa\u7840\u6570\u5b66\u548c\u9ad8\u7b49\u6570\u5b66\u4e24\u4e2a\u90e8\u5206\u3002"},"content":{"rendered":"<p>\u4e13\u5347\u672c\u6570\u5b66\u8003\u8bd5\u901a\u5e38\u5305\u62ec\u57fa\u7840\u6570\u5b66\u548c\u9ad8\u7b49\u6570\u5b66\u4e24\u4e2a\u90e8\u5206\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u53ef\u80fd\u6d89\u53ca\u5230\u7684\u4e3b\u9898\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u57fa\u7840\u6570\u5b66\uff1a<\/strong><\/p>\n<ul>\n<li><strong>\u4ee3\u6570\uff1a<\/strong> \u65b9\u7a0b\u4e0e\u4e0d\u7b49\u5f0f\u3001\u51fd\u6570\u4e0e\u56fe\u50cf\u3001\u6570\u5217\u4e0e\u6570\u5b66\u5f52\u7eb3\u6cd5\u7b49\n<p>\u65b9\u7a0b\u4e0e\u4e0d\u7b49\u5f0f\u662f\u6570\u5b66\u4e2d\u91cd\u8981\u7684\u6982\u5ff5\uff0c\u5b83\u4eec\u5728\u5404\u79cd\u6570\u5b66\u548c\u79d1\u5b66\u9886\u57df\u4e2d\u90fd\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u4e0b\u9762\u7b80\u8981\u4ecb\u7ecd\u65b9\u7a0b\u548c\u4e0d\u7b49\u5f0f\u7684\u57fa\u672c\u6982\u5ff5\uff1a<\/p>\n<h3>\u65b9\u7a0b\uff08Equations\uff09\uff1a<\/h3>\n<ol>\n<li>\n<p><strong>\u5b9a\u4e49\uff1a<\/strong> \u65b9\u7a0b\u662f\u4e00\u4e2a\u7b49\u5f0f\uff0c\u5176\u4e2d\u5305\u542b\u4e00\u4e2a\u6216\u591a\u4e2a\u672a\u77e5\u6570\uff0c\u5e76\u4e14\u8981\u6c42\u627e\u5230\u4f7f\u7b49\u5f0f\u6210\u7acb\u7684\u672a\u77e5\u6570\u7684\u503c\u3002\u65b9\u7a0b\u901a\u5e38\u5199\u6210\u5f62\u5982 <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)=0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span> \u7684\u5f62\u5f0f\uff0c\u5176\u4e2d <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd(\ufffd)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span> \u662f\u4e00\u4e2a\u5305\u542b\u672a\u77e5\u6570 <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u7684\u8868\u8fbe\u5f0f\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7c7b\u578b\uff1a<\/strong><\/p>\n<ul style=\"list-style-type: square;\">\n<li><strong>\u4e00\u6b21\u65b9\u7a0b\uff1a<\/strong> \u6700\u9ad8\u6b21\u6570\u4e3a1\u7684\u65b9\u7a0b\uff0c\u4f8b\u5982 <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd+\ufffd=0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\n<h3>\u4f8b\u9898 1\uff1a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b<\/h3>\n<p>\u89e3\u65b9\u7a0b <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">2<code>x<\/code>\u22125=3<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span>\u3002 <code>\\(y = mx + b\\)<\/code><\/p>\n<p><strong>\u89e3\u7b54\uff1a<\/strong><\/p>\n<ol>\n<li>\n<p>\u5c06 <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">2X\u22125=3<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><\/span><\/span><\/span><\/span> \u4e2d\u7684 <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u5b64\u7acb\u51fa\u6765\u3002 <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">2\ufffd\u22125+5=3+5<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span> <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">2\ufffd=8<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">8<\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<li>\n<p>\u9664\u4ee5\u7cfb\u6570 2\uff0c\u5f97\u5230 <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span><\/span> \u7684\u503c\u3002 <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd=82=4<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">8<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><\/span><\/span><\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<p>\u6240\u4ee5\uff0c\u65b9\u7a0b\u7684\u89e3\u4e3a <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd=4<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<h3>\u4f8b\u9898 2\uff1a\u4e00\u5143\u4e0d\u7b49\u5f0f<\/h3>\n<p>\u89e3\u4e0d\u7b49\u5f0f <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">3\ufffd\u22127&lt;5<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">7<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n<p><strong>\u89e3\u7b54\uff1a<\/strong><\/p>\n<ol>\n<li>\u5c06 <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">3\ufffd\u22127&lt;5<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">7<\/span><span class=\"mrel\">&lt;<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ol>\n<\/li>\n<li><strong>\u4e8c\u6b21\u65b9\u7a0b\uff1a<\/strong> \u6700\u9ad8\u6b21\u6570\u4e3a2\u7684\u65b9\u7a0b\uff0c\u4f8b\u5982 <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd2+\ufffd\ufffd+\ufffd=0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li><strong>\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff1a<\/strong> \u5305\u542b\u4e24\u4e2a\u6216\u591a\u4e2a\u7ebf\u6027\u65b9\u7a0b\u7684\u65b9\u7a0b\u7ec4\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u89e3\uff1a<\/strong> \u65b9\u7a0b\u7684\u89e3\u662f\u4f7f\u5f97\u65b9\u7a0b\u6210\u7acb\u7684\u672a\u77e5\u6570\u7684\u503c\u3002\u4e00\u5143\u65b9\u7a0b\u7684\u89e3\u662f\u4e00\u4e2a\u5177\u4f53\u7684\u6570\u503c\uff0c\u800c\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u89e3\u53ef\u4ee5\u662f\u5b9e\u6570\u6216\u590d\u6570\u3002<\/p>\n<\/li>\n<\/ol>\n<h3>\u4e0d\u7b49\u5f0f\uff08Inequalities\uff09\uff1a<\/h3>\n<ol>\n<li>\n<p><strong>\u5b9a\u4e49\uff1a<\/strong> \u4e0d\u7b49\u5f0f\u63cf\u8ff0\u4e86\u4e24\u4e2a\u8868\u8fbe\u5f0f\u4e4b\u95f4\u7684\u5927\u5c0f\u5173\u7cfb\uff0c\u53ef\u4ee5\u662f\u5927\u4e8e\uff08&gt;\uff09\u3001\u5c0f\u4e8e\uff08&lt;\uff09\u3001\u5927\u4e8e\u7b49\u4e8e\uff08\u2265\uff09\u3001\u5c0f\u4e8e\u7b49\u4e8e\uff08\u2264\uff09\u7b49\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u7c7b\u578b\uff1a<\/strong><\/p>\n<ul>\n<li><strong>\u4e00\u5143\u4e0d\u7b49\u5f0f\uff1a<\/strong> \u5305\u542b\u4e00\u4e2a\u672a\u77e5\u6570\u7684\u4e0d\u7b49\u5f0f\uff0c\u4f8b\u5982 <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd&gt;\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">&gt;<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li><strong>\u4e8c\u5143\u4e0d\u7b49\u5f0f\uff1a<\/strong> \u5305\u542b\u4e24\u4e2a\u672a\u77e5\u6570\u7684\u4e0d\u7b49\u5f0f\uff0c\u4f8b\u5982 <span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\">\ufffd\ufffd+\ufffd\ufffd\u2264\ufffd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mord mathnormal\">x<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mord mathnormal\">y<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span><\/span>\u3002<\/li>\n<li><strong>\u590d\u5408\u4e0d\u7b49\u5f0f\uff1a<\/strong> \u591a\u4e2a\u4e0d\u7b49\u5f0f\u901a\u8fc7\u903b\u8f91\u8fde\u63a5\u7b26\uff08\u5982\u201c\u4e0e\u201d\u3001\u201c\u6216\u201d\uff09\u7ec4\u5408\u800c\u6210\u7684\u4e0d\u7b49\u5f0f\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u89e3\u96c6\uff1a<\/strong> \u4e0d\u7b49\u5f0f\u7684\u89e3\u96c6\u662f\u6ee1\u8db3\u4e0d\u7b49\u5f0f\u6761\u4ef6\u7684\u6240\u6709\u53ef\u80fd\u7684\u503c\u7684\u96c6\u5408\u3002\u5bf9\u4e8e\u4e00\u5143\u4e0d\u7b49\u5f0f\uff0c\u89e3\u96c6\u901a\u5e38\u8868\u793a\u5728\u6570\u8f74\u4e0a\u7684\u4e00\u4e2a\u533a\u95f4\u3002<\/p>\n<\/li>\n<\/ol>\n<p>\u5728\u89e3\u65b9\u7a0b\u548c\u4e0d\u7b49\u5f0f\u7684\u8fc7\u7a0b\u4e2d\uff0c\u5e38\u7528\u7684\u65b9\u6cd5\u5305\u62ec\u4ee3\u6570\u8fd0\u7b97\u3001\u56e0\u5f0f\u5206\u89e3\u3001\u914d\u65b9\u6cd5\u3001\u6c42\u6839\u516c\u5f0f\u7b49\u3002\u89e3\u4e0d\u7b49\u5f0f\u65f6\u8981\u6ce8\u610f\u4fdd\u6301\u4e0d\u7b49\u5f0f\u7684\u65b9\u5411\uff0c\u5e76\u6839\u636e\u4e0d\u7b49\u5f0f\u7c7b\u578b\u9009\u62e9\u9002\u5f53\u7684\u6c42\u89e3\u65b9\u6cd5\u3002<\/p>\n<p>\u5728\u5b66\u4e60\u65b9\u7a0b\u4e0e\u4e0d\u7b49\u5f0f\u65f6\uff0c\u901a\u8fc7\u5927\u91cf\u7684\u7ec3\u4e60\u548c\u5b9e\u9645\u95ee\u9898\u7684\u5e94\u7528\uff0c\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e9b\u6982\u5ff5\u5e76\u63d0\u9ad8\u89e3\u9898\u80fd\u529b\u3002<\/p>\n<p>\u00a0<\/p>\n<ul>\n<li><strong>\u51e0\u4f55\uff1a<\/strong> \u5e73\u9762\u51e0\u4f55\u3001\u7acb\u4f53\u51e0\u4f55\u3001\u5750\u6807\u51e0\u4f55\u7b49\u3002<\/li>\n<li><strong>\u6982\u7387\u4e0e\u7edf\u8ba1\uff1a<\/strong> \u6982\u7387\u57fa\u7840\u3001\u7edf\u8ba1\u57fa\u7840\u3001\u6570\u636e\u5206\u6790\u7b49\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u9ad8\u7b49\u6570\u5b66\uff1a<\/strong><\/p>\n<ul>\n<li><strong>\u5fae\u79ef\u5206\uff1a<\/strong> \u6781\u9650\u3001\u5bfc\u6570\u3001\u79ef\u5206\u3001\u5fae\u5206\u65b9\u7a0b\u7b49\u3002<\/li>\n<li><strong>\u7ebf\u6027\u4ee3\u6570\uff1a<\/strong> \u77e9\u9635\u4e0e\u884c\u5217\u5f0f\u3001\u5411\u91cf\u7a7a\u95f4\u3001\u7279\u5f81\u503c\u4e0e\u7279\u5f81\u5411\u91cf\u7b49\u3002<\/li>\n<li><strong>\u6570\u5b66\u5206\u6790\uff1a<\/strong> \u5b9e\u6570\u3001\u7ea7\u6570\u3001\u51fd\u6570\u6781\u9650\u3001\u8fde\u7eed\u6027\u3001\u4e00\u5143\u51fd\u6570\u5fae\u79ef\u5206\u7b49\u3002<\/li>\n<\/ul>\n<\/li>\n<li>\n<p><strong>\u79bb\u6563\u6570\u5b66\uff1a<\/strong><\/p>\n<ul>\n<li><strong>\u96c6\u5408\u8bba\uff1a<\/strong> \u96c6\u5408\u8fd0\u7b97\u3001\u96c6\u5408\u5173\u7cfb\u7b49\u3002<\/li>\n<li><strong>\u903b\u8f91\u4e0e\u547d\u9898\uff1a<\/strong> \u547d\u9898\u903b\u8f91\u3001\u8c13\u8bcd\u903b\u8f91\u7b49\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p>\u4e3a\u4e86\u51c6\u5907\u4e13\u5347\u672c\u6570\u5b66\u8003\u8bd5\uff0c\u4f60\u53ef\u4ee5\u91c7\u53d6\u4ee5\u4e0b\u65b9\u6cd5\uff1a<\/p>\n<ul>\n<li><strong>\u590d\u4e60\u57fa\u7840\u77e5\u8bc6\uff1a<\/strong> \u6e29\u4e60\u4e2d\u5b66\u9636\u6bb5\u5b66\u8fc7\u7684\u4ee3\u6570\u3001\u51e0\u4f55\u3001\u6982\u7387\u4e0e\u7edf\u8ba1\u7b49\u57fa\u7840\u77e5\u8bc6\u3002<\/li>\n<li><strong>\u5b66\u4e60\u9ad8\u7b49\u6570\u5b66\uff1a<\/strong> 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