{"id":110483,"date":"2026-06-15T18:00:25","date_gmt":"2026-06-15T10:00:25","guid":{"rendered":"https:\/\/www.dongwubaike.cn\/fanhao\/?p=110483"},"modified":"2026-06-15T18:00:25","modified_gmt":"2026-06-15T10:00:25","slug":"%e5%88%9d%e4%b8%ad%e4%b8%83%e5%b9%b4%e7%ba%a7%e6%95%b0%e5%ad%a6%e7%9f%a5%e8%af%86%e7%82%b9","status":"publish","type":"post","link":"https:\/\/www.dongwubaike.cn\/fanhao\/110483.html","title":{"rendered":"\u521d\u4e2d\u4e03\u5e74\u7ea7\u6570\u5b66\u77e5\u8bc6\u70b9"},"content":{"rendered":"<p style=\"text-indent: 2em; text-align: left;\">\u77e5\u8bc6\u5728\u4e8e\u4e0d\u65ad\u7684\u79ef\u7d2f\uff0c\u624d\u80fd\u53d1\u751f\u8d28\u7684\u53d8\u5316\uff0c\u5b66\u4e60\u6570\u5b66\u603b\u7ed3\u77e5\u8bc6\u70b9\u662f\u975e\u5e38\u91cd\u8981\u7684\u4e00\u4e2a\u73af\u8282\u4e0b\u9762\u662f\u5c0f\u7f16\u4e3a\u5927\u5bb6\u6574\u7406\u7684\u5173\u4e8e\u521d\u4e2d\u4e03\u5e74\u7ea7\u6570\u5b66\u77e5\u8bc6\u70b9\uff0c\u5e0c\u671b\u5bf9\u60a8\u6709\u6240\u5e2e\u52a9!<\/p>\n<p style=\"text-indent: 2em; text-align: left;\"><strong style=\"color:#125b86\"><\/strong><strong>\u521d\u4e00\u6570\u5b66\u4e09\u89d2\u51fd\u6570\u77e5\u8bc6\u70b9<\/strong><strong style=\"color:#125b86\"><\/strong><\/p>\n<p style=\"text-indent: 2em; text-align: left;\">1\u3001\u52fe\u80a1\u5b9a\u7406\uff1a\u76f4\u89d2\u4e09\u89d2\u5f62\u4e24\u76f4\u89d2\u8fb9a\u3001b\u7684\u5e73\u65b9\u548c\u7b49\u4e8e\u659c\u8fb9c\u7684\u5e73\u65b9a2+b2=c2\u3002<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">2\u3001\u5982\u4e0b\u56fe\uff0c\u5728Rt\u25b3ABC\u4e2d\uff0c\u2220C\u4e3a\u76f4\u89d2\uff0c\u5219\u2220A\u7684\u9510\u89d2\u4e09\u89d2\u51fd\u6570\u4e3a(\u2220A\u53ef\u6362\u6210\u2220B)\uff1a<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">3\u3001\u4efb\u610f\u9510\u89d2\u7684\u6b63\u5f26\u503c\u7b49\u4e8e\u5b83\u7684\u4f59\u89d2\u7684\u4f59\u5f26\u503c;\u4efb\u610f\u9510\u89d2\u7684\u4f59\u5f26\u503c\u7b49\u4e8e\u5b83\u7684\u4f59\u89d2\u7684\u6b63\u5f26\u503c\u3002<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">4\u3001\u4efb\u610f\u9510\u89d2\u7684\u6b63\u5207\u503c\u7b49\u4e8e\u5b83\u7684\u4f59\u89d2\u7684\u4f59\u5207\u503c;\u4efb\u610f\u9510\u89d2\u7684\u4f59\u5207\u503c\u7b49\u4e8e\u5b83\u7684\u4f59\u89d2\u7684\u6b63\u5207\u503c\u3002<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">5\u30010\u00b0\u300130\u00b0\u300145\u00b0\u300160\u00b0\u300190\u00b0\u7279\u6b8a\u89d2\u7684\u4e09\u89d2\u51fd\u6570\u503c(\u91cd\u8981)<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">6\u3001\u6b63\u5f26\u3001\u4f59\u5f26\u7684\u589e\u51cf\u6027\uff1a<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">\u5f530\u00b0\u2264\u03b1\u226490\u00b0\u65f6\uff0csin\u03b1\u968f\u03b1\u7684\u589e\u5927\u800c\u589e\u5927\uff0ccos\u03b1\u968f\u03b1\u7684\u589e\u5927\u800c\u51cf\u5c0f\u3002<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">7\u3001\u6b63\u5207\u3001\u4f59\u5207\u7684\u589e\u51cf\u6027\uff1a\u5f530\u00b0&lt;\u03b1&lt;90\u00b0\u65f6\uff0ctan\u03b1\u968f\u03b1\u7684\u589e\u5927\u800c\u589e\u5927\uff0ccot\u03b1\u968f\u03b1\u7684\u589e\u5927\u800c\u51cf\u5c0f\u3002<\/p>\n<p style=\"text-indent: 2em; text-align: left;\"><strong>\u521d\u4e00\u6570\u5b66\u77e5\u8bc6\u70b9\u603b\u7ed3<\/strong><\/p>\n<p style=\"text-indent: 2em; text-align: left;\">1.\u6709\u7406\u6570\uff1a<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(1)\u51e1\u80fd\u5199\u6210 \u5f62\u5f0f\u7684\u6570\uff0c\u90fd\u662f\u6709\u7406\u6570.\u6b63\u6574\u6570\u30010\u3001\u8d1f\u6574\u6570\u7edf\u79f0\u6574\u6570;\u6b63\u5206\u6570\u3001\u8d1f\u5206\u6570\u7edf\u79f0\u5206\u6570;\u6574\u6570\u548c\u5206\u6570\u7edf\u79f0\u6709\u7406\u6570.\u6ce8\u610f\uff1a0\u5373\u4e0d\u662f\u6b63\u6570\uff0c\u4e5f\u4e0d\u662f\u8d1f\u6570;-a\u4e0d\u4e00\u5b9a\u662f\u8d1f\u6570\uff0c+a\u4e5f\u4e0d\u4e00\u5b9a\u662f\u6b63\u6570;p\u4e0d\u662f\u6709\u7406\u6570;<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(2)\u6709\u7406\u6570\u7684\u5206\u7c7b: \u2460 \u2461<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">2.\u6570\u8f74\uff1a\u6570\u8f74\u662f\u89c4\u5b9a\u4e86\u539f\u70b9\u3001\u6b63\u65b9\u5411\u3001\u5355\u4f4d\u957f\u5ea6\u7684\u4e00\u6761\u76f4\u7ebf.<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">3.\u76f8\u53cd\u6570\uff1a<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(1)\u53ea\u6709\u7b26\u53f7\u4e0d\u540c\u7684\u4e24\u4e2a\u6570\uff0c\u6211\u4eec\u8bf4\u5176\u4e2d\u4e00\u4e2a\u662f\u53e6\u4e00\u4e2a\u7684\u76f8\u53cd\u6570;0\u7684\u76f8\u53cd\u6570\u8fd8\u662f0;<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(2)\u76f8\u53cd\u6570\u7684\u548c\u4e3a0 ? a+b=0 ? a\u3001b\u4e92\u4e3a\u76f8\u53cd\u6570.<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">4.\u7edd\u5bf9\u503c\uff1a<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(1)\u6b63\u6570\u7684\u7edd\u5bf9\u503c\u662f\u5176\u672c\u8eab\uff0c0\u7684\u7edd\u5bf9\u503c\u662f0\uff0c\u8d1f\u6570\u7684\u7edd\u5bf9\u503c\u662f\u5b83\u7684\u76f8\u53cd\u6570;\u6ce8\u610f\uff1a\u7edd\u5bf9\u503c\u7684\u610f\u4e49\u662f\u6570\u8f74\u4e0a\u8868\u793a\u67d0\u6570\u7684\u70b9\u79bb\u5f00\u539f\u70b9\u7684\u8ddd\u79bb;<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(2) \u7edd\u5bf9\u503c\u53ef\u8868\u793a\u4e3a\uff1a \u6216 ;\u7edd\u5bf9\u503c\u7684\u95ee\u9898\u7ecf\u5e38\u5206\u7c7b\u8ba8\u8bba;<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">5.\u6709\u7406\u6570\u6bd4\u5927\u5c0f\uff1a(1)\u6b63\u6570\u7684\u7edd\u5bf9\u503c\u8d8a\u5927\uff0c\u8fd9\u4e2a\u6570\u8d8a\u5927;(2)\u6b63\u6570\u6c38\u8fdc\u6bd40\u5927\uff0c\u8d1f\u6570\u6c38\u8fdc\u6bd40\u5c0f;(3)\u6b63\u6570\u5927\u4e8e\u4e00\u5207\u8d1f\u6570;(4)\u4e24\u4e2a\u8d1f\u6570\u6bd4\u5927\u5c0f\uff0c\u7edd\u5bf9\u503c\u5927\u7684\u53cd\u800c\u5c0f;(5)\u6570\u8f74\u4e0a\u7684\u4e24\u4e2a\u6570\uff0c\u53f3\u8fb9\u7684\u6570\u603b\u6bd4\u5de6\u8fb9\u7684\u6570\u5927;(6)\u5927\u6570-\u5c0f\u6570 &gt; 0\uff0c\u5c0f\u6570-\u5927\u6570 &lt; 0.<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">6.\u4e92\u4e3a\u5012\u6570\uff1a\u4e58\u79ef\u4e3a1\u7684\u4e24\u4e2a\u6570\u4e92\u4e3a\u5012\u6570;\u6ce8\u610f\uff1a0\u6ca1\u6709\u5012\u6570;\u82e5 a\u22600\uff0c\u90a3\u4e48 \u7684\u5012\u6570\u662f ;\u82e5ab=1? a\u3001b\u4e92\u4e3a\u5012\u6570;\u82e5ab=-1? a\u3001b\u4e92\u4e3a\u8d1f\u5012\u6570.<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">7. \u6709\u7406\u6570\u52a0\u6cd5\u6cd5\u5219\uff1a<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(1)\u540c\u53f7\u4e24\u6570\u76f8\u52a0\uff0c\u53d6\u76f8\u540c\u7684\u7b26\u53f7\uff0c\u5e76\u628a\u7edd\u5bf9\u503c\u76f8\u52a0;<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(2)\u5f02\u53f7\u4e24\u6570\u76f8\u52a0\uff0c\u53d6\u7edd\u5bf9\u503c\u8f83\u5927\u7684\u7b26\u53f7\uff0c\u5e76\u7528\u8f83\u5927\u7684\u7edd\u5bf9\u503c\u51cf\u53bb\u8f83\u5c0f\u7684\u7edd\u5bf9\u503c;<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(3)\u4e00\u4e2a\u6570\u4e0e0\u76f8\u52a0\uff0c\u4ecd\u5f97\u8fd9\u4e2a\u6570.<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">8.\u6709\u7406\u6570\u52a0\u6cd5\u7684\u8fd0\u7b97\u5f8b\uff1a<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(1)\u52a0\u6cd5\u7684\u4ea4\u6362\u5f8b\uff1aa+b=b+a ;(2)\u52a0\u6cd5\u7684\u7ed3\u5408\u5f8b\uff1a(a+b)+c=a+(b+c).<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">9.\u6709\u7406\u6570\u51cf\u6cd5\u6cd5\u5219\uff1a\u51cf\u53bb\u4e00\u4e2a\u6570\uff0c\u7b49\u4e8e\u52a0\u4e0a\u8fd9\u4e2a\u6570\u7684\u76f8\u53cd\u6570;\u5373a-b=a+(-b).<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">10 \u6709\u7406\u6570\u4e58\u6cd5\u6cd5\u5219\uff1a<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(1)\u4e24\u6570\u76f8\u4e58\uff0c\u540c\u53f7\u4e3a\u6b63\uff0c\u5f02\u53f7\u4e3a\u8d1f\uff0c\u5e76\u628a\u7edd\u5bf9\u503c\u76f8\u4e58;<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(2)\u4efb\u4f55\u6570\u540c\u96f6\u76f8\u4e58\u90fd\u5f97\u96f6;<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(3)\u51e0\u4e2a\u6570\u76f8\u4e58\uff0c\u6709\u4e00\u4e2a\u56e0\u5f0f\u4e3a\u96f6\uff0c\u79ef\u4e3a\u96f6;\u5404\u4e2a\u56e0\u5f0f\u90fd\u4e0d\u4e3a\u96f6\uff0c\u79ef\u7684\u7b26\u53f7\u7531\u8d1f\u56e0\u5f0f\u7684\u4e2a\u6570\u51b3\u5b9a.<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">11 \u6709\u7406\u6570\u4e58\u6cd5\u7684\u8fd0\u7b97\u5f8b\uff1a<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(1)\u4e58\u6cd5\u7684\u4ea4\u6362\u5f8b\uff1aab=ba;(2)\u4e58\u6cd5\u7684\u7ed3\u5408\u5f8b\uff1a(ab)c=a(bc);<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(3)\u4e58\u6cd5\u7684\u5206\u914d\u5f8b\uff1aa(b+c)=ab+ac .<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">12.\u6709\u7406\u6570\u9664\u6cd5\u6cd5\u5219\uff1a\u9664\u4ee5\u4e00\u4e2a\u6570\u7b49\u4e8e\u4e58\u4ee5\u8fd9\u4e2a\u6570\u7684\u5012\u6570;\u6ce8\u610f\uff1a\u96f6\u4e0d\u80fd\u505a\u9664\u6570\uff0c .<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">13.\u6709\u7406\u6570\u4e58\u65b9\u7684\u6cd5\u5219\uff1a<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(1)\u6b63\u6570\u7684\u4efb\u4f55\u6b21\u5e42\u90fd\u662f\u6b63\u6570;<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(2)\u8d1f\u6570\u7684\u5947\u6b21\u5e42\u662f\u8d1f\u6570;\u8d1f\u6570\u7684\u5076\u6b21\u5e42\u662f\u6b63\u6570;\u6ce8\u610f\uff1a\u5f53n\u4e3a\u6b63\u5947\u6570\u65f6: (-a)n=-an\u6216(a -b)n=-(b-a)n , \u5f53n\u4e3a\u6b63\u5076\u6570\u65f6: (-a)n =an \u6216 (a-b)n=(b-a)n .<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">14.\u4e58\u65b9\u7684\u5b9a\u4e49\uff1a<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(1)\u6c42\u76f8\u540c\u56e0\u5f0f\u79ef\u7684\u8fd0\u7b97\uff0c\u53eb\u505a\u4e58\u65b9;<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">(2)\u4e58\u65b9\u4e2d\uff0c\u76f8\u540c\u7684\u56e0\u5f0f\u53eb\u505a\u5e95\u6570\uff0c\u76f8\u540c\u56e0\u5f0f\u7684\u4e2a\u6570\u53eb\u505a\u6307\u6570\uff0c\u4e58\u65b9\u7684\u7ed3\u679c\u53eb\u505a\u5e42;<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">15.\u79d1<a href=\"https:\/\/www.dongwubaike.cn\/fanhao\/tag\/xue-ji\" title=\"View all posts in \u5b66\u8bb0\" target=\"_blank\">\u5b66\u8bb0<\/a>\u6570\u6cd5\uff1a\u628a\u4e00\u4e2a\u5927\u4e8e10\u7684\u6570\u8bb0\u6210a\u00d710n\u7684\u5f62\u5f0f\uff0c\u5176\u4e2da\u662f\u6574\u6570\u6570\u4f4d\u53ea\u6709\u4e00\u4f4d\u7684\u6570\uff0c\u8fd9\u79cd\u8bb0\u6570\u6cd5\u53eb\u79d1\u5b66\u8bb0\u6570\u6cd5.<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">16.\u8fd1\u4f3c\u6570\u7684\u7cbe\u786e\u4f4d\uff1a\u4e00\u4e2a\u8fd1\u4f3c\u6570\uff0c\u56db\u820d\u4e94\u5165\u5230\u90a3\u4e00\u4f4d\uff0c\u5c31\u8bf4\u8fd9\u4e2a\u8fd1\u4f3c\u6570\u7684\u7cbe\u786e\u5230\u90a3\u4e00\u4f4d.<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">17.\u6709\u6548\u6570\u5b57\uff1a\u4ece\u5de6\u8fb9\u7b2c\u4e00\u4e2a\u4e0d\u4e3a\u96f6\u7684\u6570\u5b57\u8d77\uff0c\u5230\u7cbe\u786e\u7684\u4f4d\u6570\u6b62\uff0c\u6240\u6709\u6570\u5b57\uff0c\u90fd\u53eb\u8fd9\u4e2a\u8fd1\u4f3c\u6570\u7684\u6709\u6548\u6570\u5b57.<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">18.\u6df7\u5408\u8fd0\u7b97\u6cd5\u5219\uff1a\u5148\u4e58\u65b9\uff0c\u540e\u4e58\u9664\uff0c\u6700\u540e\u52a0\u51cf.<\/p>\n<p style=\"text-indent: 2em; text-align: left;\"><strong>\u4e03\u5e74\u7ea7\u6570\u5b66\u77e5\u8bc6\u70b9<\/strong><\/p>\n<p style=\"text-indent: 2em; text-align: left;\">\u96be\u70b9<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">\u4e09\u89d2\u5f62\u5185\u89d2\u548c\u5b9a\u7406\u7684\u63a8\u7406\u7684\u8fc7\u7a0b;<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">\u5728\u5177\u4f53\u7684\u56fe\u5f62\u4e2d\u4e0d\u91cd\u590d\uff0c\u4e14\u4e0d\u9057\u6f0f\u5730\u8bc6\u522b\u6240\u6709\u4e09\u89d2\u5f62;<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">\u7528\u4e09\u89d2\u5f62\u4e09\u8fb9\u4e0d\u7b49\u5173\u7cfb\u5224\u5b9a\u4e09\u6761\u7ebf\u6bb5\u53ef\u5426\u7ec4\u6210\u4e09\u89d2\u5f62\u3002<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">\u77e5\u8bc6\u70b9\u3001\u6982\u5ff5\u603b\u7ed3<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">1.\u4e09\u89d2\u5f62\uff1a\u7531\u4e0d\u5728\u540c\u4e00\u76f4\u7ebf\u4e0a\u7684\u4e09\u6761\u7ebf\u6bb5\u9996\u5c3e\u987a\u6b21\u76f8\u63a5\u6240\u7ec4\u6210\u7684\u56fe\u5f62\u53eb\u505a\u4e09\u89d2\u5f62\u3002<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">2.\u4e09\u89d2\u5f62\u7684\u5206\u7c7b<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">3.\u4e09\u89d2\u5f62\u7684\u4e09\u8fb9\u5173\u7cfb\uff1a\u4e09\u89d2\u5f62\u4efb\u610f\u4e24\u8fb9\u7684\u548c\u5927\u4e8e\u7b2c\u4e09\u8fb9\uff0c\u4efb\u610f\u4e24\u8fb9\u7684\u5dee\u5c0f\u4e8e\u7b2c\u4e09\u8fb9\u3002<\/p>\n<p style=\"text-indent: 2em; text-align: left;\">4.\u9ad8\uff1a\u4ece\u4e09\u89d2\u5f62\u7684\u4e00\u4e2a\u9876\u70b9\u5411\u5b83\u7684\u5bf9\u8fb9\u6240\u5728\u76f4\u7ebf\u4f5c\u5782\u7ebf\uff0c\u9876\u70b9\u548c\u5782\u8db3\u95f4\u7684\u7ebf\u6bb5\u53eb\u505a\u4e09\u89d2\u5f62\u7684\u9ad8\u3002<\/p>\n<p style=\"text-indent: 2em; 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