991es解方程 比如2x+7=9在计算器怎么输入 6(5-y)+13y=89 在计算器怎么输入 在线等 方程该怎么算，请百度请教请教。
6\uff085-Y\uff09+13Y=89 \u8bf7\u5927\u5bb6\u5e2e\u5fd9\u89e3\u4e00\u4e0b\u5148\u53bb\u62ec\u53f7 6*5-6*Y+13Y=89
30-6Y+13Y=89
\u5408\u5e76\u540c\u7c7b\u9879 30+(13-6)Y=89
30+7Y=89
\u79fb\u9879 7Y=89-30
7Y=49
Y=49/7
Y=7
\u65b9\u7a0b
\u7f16\u8f91
[f\u0101ng ch\u00e9ng]
\u672c\u8bcd\u6761\u9700\u8981\u8865\u5145\u66f4\u591a\u7684\u53c2\u8003\u8d44\u6599\u3002
\u767e\u5ea6\u767e\u79d1\u6240\u6709\u5185\u5bb9\u5747\u5e94\u5217\u51fa\u53c2\u8003\u8d44\u6599\u4ee5\u4f9b\u67e5\u8bc1\u3002\u6b22\u8fce\u60a8\u534f\u52a9\u7f16\u8f91\u6539\u5584\u8be5\u8bcd\u6761\u3002
\u65b9\u7a0b\uff08\u82f1\u6587\uff1aequation\uff09\u662f\u8868\u793a\u4e24\u4e2a\u6570\u5b66\u5f0f\uff08\u5982\u4e24\u4e2a\u6570\u3001\u51fd\u6570\u3001\u91cf\u3001\u8fd0\u7b97\uff09\u4e4b\u95f4\u76f8\u7b49\u5173\u7cfb\u7684\u4e00\u79cd\u7b49\u5f0f\uff0c\u662f\u542b\u6709\u672a\u77e5\u6570\u7684\u7b49\u5f0f\uff0c\u901a\u5e38\u5728\u4e24\u8005\u4e4b\u95f4\u6709\u4e00\u7b49\u53f7\u201c=\u201d\u3002\u65b9\u7a0b\u4e0d\u7528\u6309\u9006\u5411\u601d\u7ef4\u601d\u8003\uff0c\u53ef\u76f4\u63a5\u5217\u51fa\u7b49\u5f0f\u5e76\u542b\u6709\u672a\u77e5\u6570\u3002\u5b83\u5177\u6709\u591a\u79cd\u5f62\u5f0f\uff0c\u5982\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u3001\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7b49\u3002\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6570\u5b66\u3001\u7269\u7406\u7b49\u7406\u79d1\u7684\u8fd0\u7b97\u3002
\u4e2d\u6587\u540d\u65b9\u7a0b
\u5916\u6587\u540dequation
\u5b9a \u4e49\u542b\u6709\u672a\u77e5\u6570\u7684\u7b49\u5f0f
\u6240\u5c5e\u5b66\u79d1\u6570\u5b66
\u5e94\u7528\u9886\u57df\u6570\u5b66\u3001\u79d1\u5b66
\u76ee\u5f55
1\u57fa\u672c\u4fe1\u606f
2\u76f8\u5173\u6982\u5ff5
3\u6570\u5b66\u672f\u8bed
4\u89e3\u65b9\u7a0b\u7684\u4f9d\u636e\u548c\u6b65\u9aa4
▪ \u89e3\u65b9\u7a0b\u7684\u4f9d\u636e
▪ \u89e3\u65b9\u7a0b\u7684\u6b65\u9aa4
5\u65b9\u7a0b\u53f2\u8bdd
▪ \u5927\u7ea63600\u5e74\u524d
▪ \u516c\u5143825\u5e74\u5de6\u53f3
▪ \u5b8b\u5143\u65f6\u671f
6\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b
▪ \u5b9a\u4e49
▪ \u4e00\u822c\u89e3\u6cd5
7\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u6559\u5b66\u8bbe\u8ba1
▪ \u6559\u5b66\u76ee\u6807
▪ \u91cd\u70b9\u96be\u70b9
▪ \u6559\u5b66\u8fc7\u7a0b
8\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b
▪ \u5b9a\u4e49
▪ \u4e00\u822c\u89e3\u6cd5
9\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b
▪ \u5b9a\u4e49
▪ \u4e00\u822c\u5f62\u5f0f
▪ \u4e00\u822c\u89e3\u6cd5
10\u4e09\u5143\u4e00\u6b21\u65b9\u7a0b
▪ \u5b9a\u4e49
▪ \u89e3\u6cd5
▪ \u5178\u578b\u9898\u6790
11\u591a\u5143\u4e00\u6b21\u65b9\u7a0b
▪ \u6d88\u5143\u6cd5
▪ \u5176\u4ed6\u89e3\u6cd5
12\u76f4\u7ebf\u65b9\u7a0b
13\u9644\u6ce8
14\u9e21\u5154\u540c\u7b3c\u95ee\u9898
▪ \u89e3\u6cd5\u516c\u5f0f
▪ \u65b9\u7a0b\u89e3\u6cd5
15\u65b9\u7a0b\u5206\u7c7b
1\u57fa\u672c\u4fe1\u606f
\u7f16\u8f91
\u8bcd\u76ee\uff1a\u65b9\u7a0b
\u62fc\u97f3\uff1af\u0101ng ch\u00e9ng
[equation] \u8868\u793a\u4e24\u4e2a\u6570\u5b66\u5f0f(\u5982\u4e24\u4e2a\u6570\u3001\u51fd\u6570\u3001\u91cf\u3001\u8fd0\u7b97)\u4e4b\u95f4\u76f8\u7b49\u7684\u4e00\u79cd\u5f0f\u5b50,\u901a\u5e38\u5728\u4e24\u8005\u4e4b\u95f4\u6709\u4e00\u7b49\u53f7(=)
\u662f\u542b\u6709\u672a\u77e5\u6570\u7684\u7b49\u5f0f\u3002\u5982\uff1ax\uff0d2=5\uff0cx+8=y\uff0d3\u3002\u4f7f\u7b49\u5f0f\u6210\u7acb\u7684\u672a\u77e5\u6570\u7684\u503c\u79f0\u7684\u201c\u89e3\u201d\u6216\u201c\u6839\u201d\u3002\u6c42\u65b9\u7a0b\u7684\u89e3\u7684\u8fc7\u7a0b\u79f0\u4e3a\u201c\u89e3\u65b9\u7a0b\u201d\u3002\u65b9\u7a0b\u5728\u5b66\u4e60\u4e2d\u6709\u7740\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528\u3002
2\u76f8\u5173\u6982\u5ff5
\u7f16\u8f91
\u65b9\u7a0b\u5f0f\u6216\u7b80\u79f0\u65b9\u7a0b\uff0c\u662f\u542b\u6709\u672a\u77e5\u6570\u7684\u7b49\u5f0f\u3002\u5373\uff1a\u2488\u65b9\u7a0b\u4e2d\u4e00\u5b9a\u6709\u542b\u4e00\u4e2a\u6216\u4e00\u4e2a\u4ee5\u4e0a\u672a\u77e5\u6570\u7684\u4ee3\u6570\u5f0f\uff1b2.\u65b9\u7a0b\u5f0f\u662f\u7b49\u5f0f\uff0c\u4f46\u7b49\u5f0f\u4e0d\u4e00\u5b9a\u662f\u65b9\u7a0b\u3002
\u672a\u77e5\u6570\uff1a\u901a\u5e38\u8bbex.y.z\u4e3a\u672a\u77e5\u6570\uff0c\u4e5f\u53ef\u4ee5\u8bbe\u522b\u7684\u5b57\u6bcd\uff0c\u5168\u90e8\u5c0f\u5199\u5b57\u6bcd\u90fd\u53ef\u4ee5\u3002
\u201c\u6b21\u201d\uff1a\u65b9\u7a0b\u4e2d\u6b21\u7684\u6982\u5ff5\u548c\u6574\u5f0f\u7684\u201c\u6b21\u201d\u7684\u6982\u5ff5\u76f8\u4f3c\u3002\u6307\u7684\u662f\u542b\u6709\u672a\u77e5\u6570\u7684\u9879\u4e2d\uff0c\u672a\u77e5\u6570\u6b21\u6570\u6700\u9ad8\u7684\u9879\u3002\u800c\u6b21\u6570\u6700\u9ad8\u7684\u9879\uff0c\u5c31\u662f\u65b9\u7a0b\u7684\u6b21\u6570\u3002
\u201c\u89e3\u201d\uff1a\u65b9\u7a0b\u7684\u89e3\uff0c\u662f\u6307\u6240\u6709\u672a\u77e5\u6570\u7684\u603b\u79f0\uff0c\u65b9\u7a0b\u7684\u6839\u662f\u6307\u4e00\u5143\u65b9\u7a0b\u7684\u89e3\uff0c\u4e24\u8005\u901a\u5e38\u53ef\u4ee5\u901a\u7528\u3002
\u89e3\u65b9\u7a0b\uff1a\u6c42\u51fa\u65b9\u7a0b\u7684\u89e3\u7684\u8fc7\u7a0b\uff0c\u4e5f\u53ef\u4ee5\u8bf4\u662f\u6c42\u65b9\u7a0b\u4e2d\u672a\u77e5\u6570\u7684\u503c\u7684\u8fc7\u7a0b\uff0c\u6216\u8bf4\u660e\u65b9\u7a0b\u65e0\u89e3\u7684\u8fc7\u7a0b\u53eb\u89e3\u65b9\u7a0b\u3002
\u65b9\u7a0b\u4e2d\uff0c\u6052\u7b49\u5f0f\u53eb\u505a\u6052\u7b49\u65b9\u7a0b\uff0c\u77db\u76fe\u5f0f\u53eb\u505a\u77db\u76fe\u65b9\u7a0b\u3002\u5728\u672a\u77e5\u6570\u7b49\u4e8e\u67d0\u7279\u5b9a\u503c\u65f6\uff0c\u6070\u80fd\u4f7f\u7b49\u53f7\u4e24\u8fb9\u7684\u503c\u76f8\u7b49\u8005\u79f0\u4e3a\u6761\u4ef6\u65b9\u7a0b\uff0c\u4f8b\u5982 \uff0c\u5728 \u65f6\u7b49\u53f7\u6210\u7acb\u3002\u4f7f\u65b9\u7a0b\u5de6\u53f3\u4e24\u8fb9\u76f8\u7b49\u7684\u672a\u77e5\u6570\u7684\u503c\u53eb\u505a\u65b9\u7a0b\u7684\u89e3\u3002\u540c\u89e3\u65b9\u7a0b
\u5982\u679c\u4e24\u4e2a\u65b9\u7a0b\u7684\u89e3\u76f8\u540c\uff0c\u90a3\u4e48\u8fd9\u4e24\u4e2a\u65b9\u7a0b\u53eb\u505a\u540c\u89e3\u65b9\u7a0b\u3002
\u65b9\u7a0b\u7684\u540c\u89e3\u539f\u7406\uff1a
\u2488\u65b9\u7a0b\u7684\u4e24\u8fb9\u90fd\u52a0\u6216\u51cf\u540c\u4e00\u4e2a\u6570\u6216\u540c\u4e00\u4e2a\u7b49\u5f0f\u6240\u5f97\u7684\u65b9\u7a0b\u4e0e\u539f\u65b9\u7a0b\u662f\u540c\u89e3\u65b9\u7a0b\u3002
\u2489\u65b9\u7a0b\u7684\u4e24\u8fb9\u540c\u4e58\u6216\u540c\u9664\u540c\u4e00\u4e2a\u4e0d\u4e3a0\u7684\u6570\u6240\u5f97\u7684\u65b9\u7a0b\u4e0e\u539f\u65b9\u7a0b\u662f\u540c\u89e3\u65b9\u7a0b\u3002
\u6574\u5f0f\u65b9\u7a0b\uff1a\u65b9\u7a0b\u7684\u4e24\u8fb9\u90fd\u662f\u5173\u4e8e\u672a\u77e5\u6570\u7684\u6574\u5f0f\u7684\u65b9\u7a0b\u53eb\u505a\u6574\u5f0f\u65b9\u7a0b\u3002[1]
\u5206\u5f0f\u65b9\u7a0b\uff1a\u5206\u6bcd\u4e2d\u542b\u6709\u672a\u77e5\u6570\u7684\u65b9\u7a0b\u53eb\u505a\u5206\u5f0f\u65b9\u7a0b\u3002
3\u6570\u5b66\u672f\u8bed
\u7f16\u8f91
\u542b\u6709\u672a\u77e5\u6570\u7684\u7b49\u5f0f\u53eb\u65b9\u7a0b\uff0c\u8fd9\u662f\u4e2d\u5b66\u4e2d\u7684\u903b\u8f91\u5b9a\u4e49\uff0c\u65b9\u7a0b\u7684\u5b9a\u4e49\u8fd8\u6709\u51fd\u6570\u5b9a\u4e49\u6cd5\uff0c\u5173\u7cfb\u5b9a\u4e49\uff0c\u800c\u542b\u672a\u77e5\u6570\u7684\u7b49\u5f0f\u4e0d\u4e00\u5b9a\u662f\u65b9\u7a0b\uff0c\u59820x=0\u5c31\u4e0d\u662f\u65b9\u7a0b\uff0c\u5e94\u8be5\u8fd9\u6837\u5b9a\u4e49:
\u5f62\u5982\u7684\u7b49\u5f0f\uff0c\u5176\u4e2d\u548c\u662f\u5728\u5b9a\u4e49\u57df\u7684\u4ea4\u96c6\u5185\u7814\u7a76\u7684\u4e24\u4e2a\u89e3\u6790\u5f0f\uff0c\u4e14\u81f3\u5c11\u6709\u4e00\u4e2a\u4e0d\u662f\u5e38\u6570\u3002
4\u89e3\u65b9\u7a0b\u7684\u4f9d\u636e\u548c\u6b65\u9aa4
\u7f16\u8f91
\u89e3\u65b9\u7a0b\u7684\u4f9d\u636e
1.\u79fb\u9879\uff1a\u628a\u65b9\u7a0b\u4e2d\u7684\u67d0\u4e9b\u9879\u6539\u53d8\u7b26\u53f7\u540e\uff0c\u4ece\u65b9\u7a0b\u7684\u4e00\u8fb9\u79fb\u5230\u53e6\u4e00\u8fb9\uff1b
2.\u7b49\u5f0f\u7684\u57fa\u672c\u6027\u8d28
\u6027\u8d281
\u7b49\u5f0f\u4e24\u8fb9\u540c\u65f6\u52a0(\u6216\u51cf)\u540c\u4e00\u4e2a\u6570\u6216\u540c\u4e00\u4e2a\u4ee3\u6570\u5f0f\uff0c\u6240\u5f97\u7684\u7ed3\u679c\u4ecd\u662f\u7b49\u5f0f\u3002\u7528\u5b57\u6bcd\u8868\u793a\u4e3a\uff1a\u82e5a=b\uff0cc\u4e3a\u4e00\u4e2a\u6570\u6216\u4e00\u4e2a\u4ee3\u6570\u5f0f\u3002\u5219\uff1a(1) a+c=b+c (2) a-c=b-c
\u6027\u8d282
\u7b49\u5f0f\u7684\u4e24\u8fb9\u540c\u65f6\u4e58\u6216\u9664\u4ee5\u540c\u4e00\u4e2a\u4e0d\u4e3a0\u7684\u6570\u6240\u5f97\u7684\u7ed3\u679c\u4ecd\u662f\u7b49\u5f0f\u3002
\u7528\u5b57\u6bcd\u8868\u793a\u4e3a\uff1a\u82e5a=b\uff0cc\u4e3a\u4e00\u4e2a\u6570\u6216\u4e00\u4e2a\u4ee3\u6570\u5f0f\uff08\u4e0d\u4e3a0\uff09\u3002\u5219\uff1a
a\u00d7c=b\u00d7c a\u00f7c=b\u00f7c
\u6027\u8d283
\u82e5a=b,\u5219b=a\uff08\u7b49\u5f0f\u7684\u5bf9\u79f0\u6027\uff09\u3002
\u6027\u8d284
\u82e5a=b,b=c\u5219a=c\uff08\u7b49\u5f0f\u7684\u4f20\u9012\u6027\uff09\u3002
3.\u5408\u5e76\u540c\u7c7b\u9879\uff1b
\u89e3\u65b9\u7a0b\u7684\u6b65\u9aa4
6\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b
\u7f16\u8f91
\u5b9a\u4e49
\u53ea\u542b\u6709\u4e00\u4e2a\u672a\u77e5\u6570\uff0c\u4e14\u672a\u77e5\u6570\u6b21\u6570\u662f\u4e00\u7684\u6574\u5f0f\u65b9\u7a0b\u53eb\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\uff08linear equation with one unknown\uff09\u3002\u901a\u5e38\u5f62\u5f0f\u662fax+b=0(a\uff0cb\u4e3a\u5e38\u6570\uff0c\u4e14a\u22600\uff09\u3002
\u4e00\u822c\u89e3\u6cd5
\u53bb\u5206\u6bcd \u65b9\u7a0b\u4e24\u8fb9\u540c\u65f6\u4e58\u5404\u5206\u6bcd\u7684\u6700\u5c0f\u516c\u500d\u6570\u3002
\u53bb\u62ec\u53f7 \u4e00\u822c\u5148\u53bb\u5c0f\u62ec\u53f7\uff0c\u518d\u53bb\u4e2d\u62ec\u53f7\uff0c\u6700\u540e\u53bb\u5927\u62ec\u53f7\u3002\u4f46\u987a\u5e8f\u6709\u65f6\u53ef\u4f9d\u636e\u60c5\u51b5\u800c\u5b9a\u4f7f\u8ba1\u7b97\u7b80\u4fbf\u3002\u53ef\u6839\u636e\u4e58\u6cd5\u5206\u914d\u5f8b\u3002
\u79fb\u9879 \u628a\u65b9\u7a0b\u4e2d\u542b\u6709\u672a\u77e5\u6570\u7684\u9879\u79fb\u5230\u65b9\u7a0b\u7684\u53e6\u4e00\u8fb9\uff0c\u5176\u4f59\u5404\u9879\u79fb\u5230\u65b9\u7a0b\u7684\u53e6\u4e00\u8fb9\u79fb\u9879\u65f6\u522b\u5fd8\u8bb0\u4e86\u8981\u53d8\u53f7\u3002(\u4e00\u822c\u90fd\u662f\u8fd9\u6837\uff1a\uff08\u6bd4\u65b9\uff09\u4ece 5x=4x+8 \u5f97\u5230 5x - 4x=8 \uff1b\u628a\u672a\u77e5\u6570\u79fb\u5230\u4e00\u8d77\uff01
\u5408\u5e76\u540c\u7c7b\u9879 \u5c06\u539f\u65b9\u7a0b\u5316\u4e3aax=b(a\u22600)\u7684\u5f62\u5f0f\u3002
\u5316\u7cfb\u6570\u4e3a\u4e00 \u65b9\u7a0b\u4e24\u8fb9\u540c\u65f6\u9664\u4ee5\u672a\u77e5\u6570\u7684\u7cfb\u6570\u3002
\u5f97\u51fa\u65b9\u7a0b\u7684\u89e3\u3002
\u91cd\u70b9\u96be\u70b9
\u7eb5\u89c2\u4f8b1\u7684\u8fd9\u4e24\u79cd\u89e3\u6cd5\uff0c\u5f88\u660e\u663e\uff0c\u7b97\u672f\u65b9\u6cd5\u4e0d\u6613\u601d\u8003\uff0c\u800c\u5e94\u7528\u8bbe\u672a\u77e5\u6570\uff0c\u5217\u51fa\u65b9\u7a0b\u5e76\u901a\u8fc7\u89e3\u65b9\u7a0b\u6c42\u5f97\u5e94\u7528\u9898\u7684\u89e3\u7684\u65b9\u6cd5\uff0c\u6709\u4e00\u79cd\u5316\u96be\u4e3a\u6613\u4e4b\u611f\uff0c\u8fd9\u5c31\u662f\u6211\u4eec\u5b66\u4e60\u8fd0\u7528\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u89e3\u5e94\u7528\u9898\u7684\u76ee\u7684\u4e4b\u4e00\uff0e
\u6211\u4eec\u77e5\u9053\u65b9\u7a0b\u662f\u4e00\u4e2a\u542b\u6709\u672a\u77e5\u6570\u7684\u7b49\u5f0f\uff0c\u800c\u7b49\u5f0f\u8868\u793a\u4e86\u4e00\u4e2a\u76f8\u7b49\u5173\u7cfb\uff0e\u56e0\u6b64\u5bf9\u4e8e\u4efb\u4f55\u4e00\u4e2a\u5e94\u7528\u9898\u4e2d\u63d0\u4f9b\u7684\u6761\u4ef6\uff0c\u5e94\u9996\u5148\u4ece\u4e2d\u627e\u51fa\u4e00\u4e2a\u76f8\u7b49\u5173\u7cfb\uff0c\u7136\u540e\u518d\u5c06\u8fd9\u4e2a\u76f8\u7b49\u5173\u7cfb\u8868\u793a\u6210\u65b9\u7a0b\uff0e
\u672c\u8282\u8bfe\uff0c\u6211\u4eec\u5c31\u901a\u8fc7\u5b9e\u4f8b\u6765\u8bf4\u660e\u600e\u6837\u5bfb\u627e\u4e00\u4e2a\u76f8\u7b49\u7684\u5173\u7cfb\u548c\u628a\u8fd9\u4e2a\u76f8\u7b49\u5173\u7cfb\u8f6c\u5316\u4e3a\u65b9\u7a0b\u7684\u65b9\u6cd5\u548c\u6b65\u9aa4\uff0e
\u4e8c\u3001\u5e08\u751f\u5171\u540c\u5206\u6790\u3001\u7814\u7a76\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u89e3\u7b80\u5355\u5e94\u7528\u9898\u7684\u65b9\u6cd5\u548c\u6b65\u9aa4
\u4f8b2 \u67d0\u9762\u7c89\u4ed3\u5e93\u5b58\u653e\u7684\u9762\u7c89\u8fd0\u51fa 15%\u540e\uff0c\u8fd8\u5269\u4f5942500\u5343\u514b\uff0c\u8fd9\u4e2a\u4ed3\u5e93\u539f\u6765\u6709\u591a\u5c11\u9762\u7c89\uff1f
\u5e08\u751f\u5171\u540c\u5206\u6790\uff1a
\u672c\u9898\u4e2d\u7ed9\u51fa\u7684\u5df2\u77e5\u91cf\u548c\u672a\u77e5\u91cf\u5404\u662f\u4ec0\u4e48\uff1f
\u5df2\u77e5\u91cf\u4e0e\u672a\u77e5\u91cf\u4e4b\u95f4\u5b58\u5728\u7740\u600e\u6837\u7684\u76f8\u7b49\u5173\u7cfb\uff1f(\u539f\u6765\u91cd\u91cf-\u8fd0\u51fa\u91cd\u91cf=\u5269\u4f59\u91cd\u91cf)
\u82e5\u8bbe\u539f\u6765\u9762\u7c89\u6709x\u5343\u514b\uff0c\u5219\u8fd0\u51fa\u9762\u7c89\u53ef\u8868\u793a\u4e3a\u591a\u5c11\u5343\u514b\uff1f\u5229\u7528\u4e0a\u8ff0\u76f8\u7b49\u5173\u7cfb\uff0c\u5982\u4f55\u5e03\u5217\u65b9\u7a0b\uff1f
\u4e0a\u8ff0\u5206\u6790\u8fc7\u7a0b\u53ef\u5217\u8868\u5982\u4e0b\uff1a
\u89e3\uff1a\u8bbe\u539f\u6765\u6709x\u5343\u514b\u9762\u7c89\uff0c\u90a3\u4e48\u8fd0\u51fa\u4e8615%x\u5343\u514b\uff0c\u7531\u9898\u610f\uff0c\u5f97x-15%x=42500\uff0c
x-15%x=42500
\u89e3\uff1a(1-15%)x=42500
85%x=42500
x=42500\u00f785%
x=50000
\u6240\u4ee5 x=50000\uff0e
\u7b54\uff1a\u539f\u6765\u6709 50000\u5343\u514b\u9762\u7c89\uff0e
\u6b64\u65f6\uff0c\u8ba9\u5b66\u751f\u8ba8\u8bba\uff1a\u672c\u9898\u7684\u76f8\u7b49\u5173\u7cfb\u9664\u4e86\u4e0a\u8ff0\u8868\u8fbe\u5f62\u5f0f\u4ee5\u5916\uff0c\u662f\u5426\u8fd8\u6709\u5176\u4ed6\u8868\u8fbe\u5f62\u5f0f\uff1f\u82e5\u6709\uff0c\u662f\u4ec0\u4e48\uff1f
(\u8fd8\u6709\uff0c\u539f\u6765\u91cd\u91cf=\u8fd0\u51fa\u91cd\u91cf+\u5269\u4f59\u91cd\u91cf\uff1b\u539f\u6765\u91cd\u91cf-\u5269\u4f59\u91cd\u91cf=\u8fd0\u51fa\u91cd\u91cf)
\u6559\u5e08\u5e94\u6307\u51fa\uff1a(1)\u8fd9\u4e24\u79cd\u76f8\u7b49\u5173\u7cfb\u7684\u8868\u8fbe\u5f62\u5f0f\u4e0e\u201c\u539f\u6765\u91cd\u91cf-\u8fd0\u51fa\u91cd\u91cf=\u5269\u4f59\u91cd\u91cf\u201d\uff0c\u867d\u5f62\u5f0f\u4e0a\u4e0d\u540c\uff0c\u4f46\u5b9e\u8d28\u662f\u4e00\u6837\u7684\uff0c\u53ef\u4ee5\u4efb\u610f\u9009\u62e9\u5176\u4e2d\u7684\u4e00\u4e2a\u76f8\u7b49\u5173\u7cfb\u6765\u5217\u65b9\u7a0b
(2)\u4f8b2\u7684\u89e3\u65b9\u7a0b\u8fc7\u7a0b\u8f83\u4e3a\u7b80\u6377\uff0c\u540c\u5b66\u5e94\u6ce8\u610f\u6a21\u4eff\uff0e
\u4f9d\u636e\u4f8b2\u7684\u5206\u6790\u4e0e\u89e3\u7b54\u8fc7\u7a0b\uff0c\u9996\u5148\u8bf7\u540c\u5b66\u4eec\u601d\u8003\u5217\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u89e3\u5e94\u7528\u9898\u7684\u65b9\u6cd5\u548c\u6b65\u9aa4\uff1b\u7136\u540e\uff0c\u91c7\u53d6\u63d0\u95ee\u7684\u65b9\u5f0f\uff0c\u8fdb\u884c\u53cd\u9988\uff1b\u6700\u540e\uff0c\u6839\u636e\u5b66\u751f\u603b\u7ed3\u7684\u60c5\u51b5\uff0c\u6559\u5e08\u603b\u7ed3\u5982\u4e0b\uff1a
(1)\u4ed4\u7ec6\u5ba1\u9898\uff0c\u900f\u5f7b\u7406\u89e3\u9898\u610f\uff0e\u5373\u5f04\u6e05\u5df2\u77e5\u91cf\u3001\u672a\u77e5\u91cf\u53ca\u5176\u76f8\u4e92\u5173\u7cfb\uff1b\u7528\u5b57\u6bcd(\u5982x)\u8868\u793a\u9898\u4e2d\u7684\u672a\u77e5\u6570
(2)\u6839\u636e\u9898\u610f\u627e\u51fa\u76f8\u7b49\u5173\u7cfb\uff0e(\u8fd9\u662f\u5173\u952e\u4e00\u6b65)
(3)\u6839\u636e\u76f8\u7b49\u5173\u7cfb\uff0c\u6b63\u786e\u5217\u51fa\u65b9\u7a0b\uff0e\u5373\u6240\u5217\u7684\u65b9\u7a0b\u5e94\u6ee1\u8db3\u4e24\u8fb9\u7684\u91cf\u8981\u76f8\u7b49\uff1b\u65b9\u7a0b\u4e24\u8fb9\u7684\u4ee3\u6570\u5f0f\u7684\u5355\u4f4d\u8981\u76f8\u540c\uff1b\u9898\u4e2d\u6761\u4ef6\u5e94\u5145\u5206\u5229\u7528\uff0c\u4e0d\u80fd\u6f0f\u4e5f\u4e0d\u80fd\u5c06\u4e00\u4e2a\u6761\u4ef6\u91cd\u590d\u5229\u7528\u7b49
(4)\u6c42\u51fa\u6240\u5217\u65b9\u7a0b\u7684\u89e3
(5)\u68c0\u9a8c\u540e\u660e\u786e\u5730\u3001\u5b8c\u6574\u5730\u5199\u51fa\u7b54\u6848\uff0e\u8fd9\u91cc\u8981\u6c42\u7684\u68c0\u9a8c\u5e94\u662f\uff0c\u68c0\u9a8c\u6240\u6c42\u51fa\u7684\u89e3\u65e2\u80fd\u4f7f\u65b9\u7a0b\u6210\u7acb\uff0c\u53c8\u80fd\u4f7f\u5e94\u7528\u9898\u6709\u610f\u4e49\uff0e
8\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b
\u7f16\u8f91
\u4eba\u6559\u72487\u5e74\u7ea7\u6570\u5b66\u4e0b\u518c\u7b2c\u56db\u7ae0\u4f1a\u5b66\u5230\uff0c\u5180\u6559\u72487\u5e74\u7ea7\u6570\u5b66\u4e0b\u518c\u7b2c\u4e5d\u7ae0\u4f1a\u5b66\u5230\u3002\u5728\u4eba\u6559\u7248\u4e5d\u5e74\u7ea7\u4e0a\u82f1\u8bed\u8bb2\u7231\u56e0\u65af\u5766\u65f6\u4e5f\u4f1a\u6d89\u53ca
\u5b9a\u4e49
\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u5b9a\u4e49\uff1a\u4e00\u4e2a\u542b\u6709\u4e24\u4e2a\u672a\u77e5\u6570\uff0c\u5e76\u4e14\u672a\u77e5\u6570\u7684\u6307\u6570\u90fd\u662f1\u7684\u6574\u5f0f\u65b9\u7a0b\uff0c\u53eb\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b(linear equation of two unknowns)\u3002
\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7ec4\u5b9a\u4e49\uff1a\u7531\u4e24\u4e2a\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7ec4\u6210\u7684\u65b9\u7a0b\u7ec4\uff0c\u53eb\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7ec4(system of linear equation of two unknowns)\u3002
\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7684\u89e3\uff1a\u4f7f\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u4e24\u8fb9\u7684\u503c\u76f8\u7b49\u7684\u4e24\u4e2a\u672a\u77e5\u6570\u7684\u503c\uff0c\u53eb\u505a\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7684\u89e3\u3002
\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7ec4\u7684\u89e3\uff1a\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7ec4\u7684\u4e24\u4e2a\u516c\u5171\u89e3\uff0c\u53eb\u505a\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7ec4\u7684\u89e3\u3002
\u4e00\u822c\u89e3\u6cd5
\u6d88\u5143\uff1a\u5c06\u65b9\u7a0b\u7ec4\u4e2d\u7684\u672a\u77e5\u6570\u4e2a\u6570\u7531\u591a\u5316\u5c11\uff0c\u9010\u4e00\u89e3\u51b3\u3002
\u6d88\u5143\u7684\u65b9\u6cd5\u6709\u4e24\u79cd\uff1a
\u4ee3\u5165\u6d88\u5143
\u4f8b\uff1a\u89e3\u65b9\u7a0b\u7ec4x+y=5\u2460 6x+13y=89\u2461
\u89e3\uff1a\u7531\u2460\u5f97x=5-y\u2462 \u628a\u2462\u5e26\u5165\u2461\uff0c\u5f976(5-y)+13y=89\uff0c\u89e3\u5f97y=59/7
\u628ay=59/7\u5e26\u5165\u2462\uff0c\u5f97x=5-59/7\uff0c\u5373x=-24/7
\u2234x=-24/7\uff0cy=59/7
\u8fd9\u79cd\u89e3\u6cd5\u5c31\u662f\u4ee3\u5165\u6d88\u5143\u6cd5\u3002
\u52a0\u51cf\u6d88\u5143
\u4f8b\uff1a\u89e3\u65b9\u7a0b\u7ec4x+y=9\u2460 x-y=5\u2461
\u89e3\uff1a\u2460+\u2461\uff0c\u5f972x=14\uff0c\u5373x=7
\u628ax=7\u5e26\u5165\u2460\uff0c\u5f977+y=9\uff0c\u89e3\u5f97y=2
\u2234x=7\uff0cy=2
\u8fd9\u79cd\u89e3\u6cd5\u5c31\u662f\u52a0\u51cf\u6d88\u5143\u6cd5\u3002
\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7ec4\u7684\u89e3\u6709\u4e09\u79cd\u60c5\u51b5\uff1a
1.\u6709\u4e00\u7ec4\u89e3
\u5982\u65b9\u7a0b\u7ec4x+y=5\u2460 6x+13y=89\u2461\u7684\u89e3\u4e3ax=-24/7\uff0cy=59/7\u3002
2.\u6709\u65e0\u6570\u7ec4\u89e3
\u5982\u65b9\u7a0b\u7ec4x+y=6\u2460 2x+2y=12\u2461\uff0c\u56e0\u4e3a\u8fd9\u4e24\u4e2a\u65b9\u7a0b\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a\u65b9\u7a0b\uff08\u4ea6\u79f0\u4f5c\u201c\u65b9\u7a0b\u6709\u4e24\u4e2a\u76f8\u7b49\u7684\u5b9e\u6570\u6839\u201d\uff09\uff0c\u6240\u4ee5\u6b64\u7c7b\u65b9\u7a0b\u7ec4\u6709\u65e0\u6570\u7ec4\u89e3\u3002
3.\u65e0\u89e3
\u5982\u65b9\u7a0b\u7ec4x+y=4\u2460 2x+2y=10\u2461\uff0c\u56e0\u4e3a\u65b9\u7a0b\u2461\u5316\u7b80\u540e\u4e3ax+y=5\uff0c\u8fd9\u4e0e\u65b9\u7a0b\u2460\u76f8\u77db\u76fe\uff0c\u6240\u4ee5\u6b64\u7c7b\u65b9\u7a0b\u7ec4\u65e0\u89e3\u3002
9\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b
\u7f16\u8f91
\u5b9a\u4e49
\u542b\u6709\u4e00\u4e2a\u672a\u77e5\u6570\uff0c\u5e76\u4e14\u672a\u77e5\u6570\u7684\u6700\u9ad8\u6b21\u6570\u662f2\u7684\u6574\u5f0f\u65b9\u7a0b\uff0c\u8fd9\u6837\u7684\u65b9\u7a0b\u53eb\u505a\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b(quadratic equation in one unknown)\u3002
\u7531\u4e00\u6b21\u65b9\u7a0b\u5230\u4e8c\u6b21\u65b9\u7a0b\u662f\u4e2a\u8d28\u7684\u8f6c\u53d8\uff0c\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u4e8c\u6b21\u65b9\u7a0b\u65e0\u8bba\u662f\u5728\u6982\u5ff5\u4e0a\u8fd8\u662f\u89e3\u6cd5\u4e0a\u90fd\u6bd4\u4e00\u6b21\u65b9\u7a0b\u8981\u590d\u6742\u5f97\u591a\u3002
\u4e00\u822c\u5f62\u5f0f
(a\u22600)
\u4e00\u822c\u89e3\u6cd5
\u4e00\u822c\u89e3\u6cd5\u6709\u56db\u79cd\uff1a
\u2488\u516c\u5f0f\u6cd5\uff08\u76f4\u63a5\u5f00\u5e73\u65b9\u6cd5\uff09
\u2489\u914d\u65b9\u6cd5
3.\u56e0\u5f0f\u5206\u89e3\u6cd5
4.\u5341\u5b57\u76f8\u4e58\u6cd5
\u5341\u5b57\u76f8\u4e58\u6cd5\u80fd\u628a\u67d0\u4e9b\u4e8c\u6b21\u4e09\u9879\u5f0f\u5206\u89e3\u56e0\u5f0f\u3002\u8fd9\u79cd\u65b9\u6cd5\u7684\u5173\u952e\u662f\u628a\u4e8c\u6b21\u9879\u7cfb\u6570a\u5206\u89e3\u6210\u4e24\u4e2a\u56e0\u6570a1,a2\u7684\u79efa1\u00b7a2\uff0c\u628a\u5e38\u6570\u9879c\u5206\u89e3\u6210\u4e24\u4e2a\u56e0\u6570c1,c2\u7684\u79efc1\u00b7c2\uff0c\u5e76\u4f7fa1c2+a2c1\u6b63\u597d\u662f\u4e00\u6b21\u9879b\uff0c\u90a3\u4e48\u53ef\u4ee5\u76f4\u63a5\u5199\u6210\u7ed3\u679c:\u5728\u8fd0\u7528\u8fd9\u79cd\u65b9\u6cd5\u5206\u89e3\u56e0\u5f0f\u65f6\uff0c\u8981\u6ce8\u610f\u89c2\u5bdf\uff0c\u5c1d\u8bd5\uff0c\u5e76\u4f53\u4f1a\u5b83\u5b9e\u8d28\u662f\u4e8c\u9879\u5f0f\u4e58\u6cd5\u7684\u9006\u8fc7\u7a0b\u3002\u5f53\u9996\u9879\u7cfb\u6570\u4e0d\u662f1\u65f6\uff0c\u5f80\u5f80\u9700\u8981\u591a\u6b21\u8bd5\u9a8c\uff0c\u52a1\u5fc5\u6ce8\u610f\u5404\u9879\u7cfb\u6570\u7684\u7b26\u53f7\u3002
\u4f8b1 \u628a\u5206\u89e3\u56e0\u5f0f\u3002
\u5206\u6790\uff1a\u5148\u5206\u89e3\u4e8c\u6b21\u9879\u7cfb\u6570\uff0c\u5206\u522b\u5199\u5728\u5341\u5b57\u4ea4\u53c9\u7ebf\u7684\u5de6\u4e0a\u89d2\u548c\u5de6\u4e0b\u89d2\uff0c\u518d\u5206\u89e3\u5e38\u6570\u9879\uff0c\u5206
\u522b\u5199\u5728\u5341\u5b57\u4ea4\u53c9\u7ebf\u7684\u53f3\u4e0a\u89d2\u548c\u53f3\u4e0b\u89d2\uff0c\u7136\u540e\u4ea4\u53c9\u76f8\u4e58\uff0c\u6c42\u4ee3\u6570\u548c\uff0c\u4f7f\u5176\u7b49\u4e8e\u4e00\u6b21\u9879\u7cfb\u6570.
\u5206\u89e3\u4e8c\u6b21\u9879\u7cfb\u6570(\u53ea\u53d6\u6b63\u56e0\u6570)\uff1a
2=1\u00d72=2\u00d71\uff1b
\u5206\u89e3\u5e38\u6570\u9879\uff1a
3=1\u00d73=3\u00d71=(-3)\u00d7(-1)=(-1)\u00d7(-3).
\u7528\u753b\u5341\u5b57\u4ea4\u53c9\u7ebf\u65b9\u6cd5\u8868\u793a\u4e0b\u5217\u56db\u79cd\u60c5\u51b5\uff1a
1 1
\u2573
2 3
1\u00d73+2\u00d71
=5
1 3
\u2573
2 1
1\u00d71+2\u00d73
=7
1 -1
\u2573
2 -3
1\u00d7(-3)+2\u00d7(-1)
=-5
1 -3
\u2573
2 -1
1\u00d7(-1)+2\u00d7(-3)
=-7
\u7ecf\u8fc7\u89c2\u5bdf\uff0c\u7b2c\u56db\u79cd\u60c5\u51b5\u662f\u6b63\u786e\u7684\uff0c\u8fd9\u662f\u56e0\u4e3a\u4ea4\u53c9\u76f8\u4e58\u540e\uff0c\u4e24\u9879\u4ee3\u6570\u548c\u6070\u7b49\u4e8e\u4e00\u6b21\u9879\u7cfb\u6570\uff0d7.
\u89e3.
\u4e00\u822c\u5730\uff0c\u5bf9\u4e8e\u4e8c\u6b21\u4e09\u9879\u5f0fax2+bx+c(a\u22600)\uff0c\u5982\u679c\u4e8c\u6b21\u9879\u7cfb\u6570a\u53ef\u4ee5\u5206\u89e3\u6210\u4e24\u4e2a\u56e0\u6570\u4e4b\u79ef\uff0c\u5373a=a1a2\uff0c\u5e38\u6570\u9879c\u53ef\u4ee5\u5206\u89e3\u6210\u4e24\u4e2a\u56e0\u6570\u4e4b\u79ef\uff0c\u5373c=c1c2\uff0c\u628aa1\uff0ca2\uff0cc1\uff0cc2\uff0c\u6392\u5217\u5982\u4e0b\uff1a
a1 c1
\u2573
a2 c2
a1c2+a2c1
\u6309\u659c\u7ebf\u4ea4\u53c9\u76f8\u4e58\uff0c\u518d\u76f8\u52a0\uff0c\u5f97\u5230a1c2+a2c1\uff0c\u82e5\u5b83\u6b63\u597d\u7b49\u4e8e\u4e8c\u6b21\u4e09\u9879\u5f0fax2+bx+c\u7684\u4e00\u6b21\u9879\u7cfb\u6570b\uff0c\u5373a1c2+a2c1=b\uff0c\u90a3\u4e48\u4e8c\u6b21\u4e09\u9879\u5f0f\u5c31\u53ef\u4ee5\u5206\u89e3\u4e3a\u4e24\u4e2a\u56e0\u5f0fa1x+c1\u4e0ea2x+c2\u4e4b\u79ef\uff0c\u5373
ax2+bx+c=(a1x+c1)(a2x+c2).
\u50cf\u8fd9\u79cd\u501f\u52a9\u753b\u5341\u5b57\u4ea4\u53c9\u7ebf\u5206\u89e3\u7cfb\u6570\uff0c\u4ece\u800c\u5e2e\u52a9\u6211\u4eec\u628a\u4e8c\u6b21\u4e09\u9879\u5f0f\u5206\u89e3\u56e0\u5f0f\u7684\u65b9\u6cd5\uff0c\u901a\u5e38\u53eb\u505a\u5341\u5b57\u76f8\u4e58\u6cd5\u3002
\u4f8b2 \u628a\u5206\u89e3\u56e0\u5f0f.
\u5206\u6790\uff1a\u6309\u7167\u4f8b1\u7684\u65b9\u6cd5\uff0c\u5206\u89e3\u4e8c\u6b21\u9879\u7cfb\u65706\u53ca\u5e38\u6570\u9879-5\uff0c\u628a\u5b83\u4eec\u5206\u522b\u6392\u5217\uff0c\u53ef\u67098\u79cd\u4e0d\u540c\u7684\u6392\u5217\u65b9\u6cd5\uff0c\u5176\u4e2d\u7684\u4e00\u79cd
2 1
\u2573
3 -5
2\u00d7(-5)+3\u00d71=-7
\u662f\u6b63\u786e\u7684\uff0c\u56e0\u6b64\u539f\u591a\u9879\u5f0f\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f\u3002
\u89e3
\u6307\u51fa\uff1a\u901a\u8fc7\u4f8b1\u548c\u4f8b2\u53ef\u4ee5\u770b\u5230\uff0c\u8fd0\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u628a\u4e00\u4e2a\u4e8c\u6b21\u9879\u7cfb\u6570\u4e0d\u662f1\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\uff0c\u5f80\u5f80\u8981\u7ecf\u8fc7\u591a\u6b21\u89c2\u5bdf\uff0c\u624d\u80fd\u786e\u5b9a\u662f\u5426\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f.
\u5bf9\u4e8e\u4e8c\u6b21\u9879\u7cfb\u6570\u662f1\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u4e5f\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f\uff0c\u8fd9\u65f6\u53ea\u9700\u8003\u8651\u5982\u4f55\u628a\u5e38\u6570\u9879\u5206\u89e3\u56e0\u6570\u3002\u4f8b\u5982\u628a\u5206\u89e3\u56e0\u5f0f\uff0c\u5341\u5b57\u76f8\u4e58\u6cd5\u662f
1 -3
\u2573
1 5
1\u00d75+1\u00d7(-3)=2
\u6240\u4ee5.
\u4f8b3 \u628a\u5206\u89e3\u56e0\u5f0f\u3002
\u5206\u6790\uff1a\u8fd9\u4e2a\u591a\u9879\u5f0f\u53ef\u4ee5\u770b\u4f5c\u662f\u5173\u4e8ex\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u628a-8y^2\u770b\u4f5c\u5e38\u6570\u9879\uff0c\u5728\u5206\u89e3\u4e8c\u6b21\u9879\u53ca\u5e38\u6570\u9879\u7cfb\u6570\u65f6\uff0c\u53ea\u9700\u5206\u89e35\u4e0e-8\uff0c\u7528\u5341\u5b57\u4ea4\u53c9\u7ebf\u5206\u89e3\u540e\uff0c\u7ecf\u8fc7\u89c2\u5bdf\uff0c\u9009\u53d6\u5408\u9002\u7684\u4e00\u7ec4\uff0c\u5373
1 2
\u2573
5 -4
1\u00d7(-4)+5\u00d72=6
\u89e3.
\u6307\u51fa\uff1a\u539f\u5f0f\u5206\u89e3\u4e3a\u4e24\u4e2a\u5173\u4e8ex\uff0cy\u7684\u4e00\u6b21\u5f0f\u3002
\u4f8b4 \u628a(x-y)(2x-2y-3)-2\u5206\u89e3\u56e0\u5f0f.
\u5206\u6790\uff1a\u8fd9\u4e2a\u591a\u9879\u5f0f\u662f\u4e24\u4e2a\u56e0\u5f0f\u4e4b\u79ef\u4e0e\u53e6\u4e00\u4e2a\u56e0\u6570\u4e4b\u5dee\u7684\u5f62\u5f0f\uff0c\u53ea\u6709\u5148\u8fdb\u884c\u591a\u9879\u5f0f\u7684\u4e58\u6cd5\u8fd0\u7b97\uff0c\u628a\u53d8\u5f62\u540e\u7684\u591a\u9879\u5f0f\u518d\u56e0\u5f0f\u5206\u89e3\u3002
\u95ee\uff1a\u4e24\u4e0a\u4e58\u79ef\u7684\u56e0\u5f0f\u662f\u4ec0\u4e48\u7279\u70b9\uff0c\u7528\u4ec0\u4e48\u65b9\u6cd5\u8fdb\u884c\u591a\u9879\u5f0f\u7684\u4e58\u6cd5\u8fd0\u7b97\u6700\u7b80\u4fbf?
\u7b54\uff1a\u7b2c\u4e8c\u4e2a\u56e0\u5f0f\u4e2d\u7684\u524d\u4e24\u9879\u5982\u679c\u63d0\u51fa\u516c\u56e0\u5f0f2\uff0c\u5c31\u53d8\u4e3a2(x-y)\uff0c\u5b83\u662f\u7b2c\u4e00\u4e2a\u56e0\u5f0f\u7684\u4e8c\u500d\uff0c\u7136\u540e\u628a(x-y)\u770b\u4f5c\u4e00\u4e2a\u6574\u4f53\u8fdb\u884c\u4e58\u6cd5\u8fd0\u7b97\uff0c\u53ef\u628a\u539f\u591a\u9879\u5f0f\u53d8\u5f62\u4e3a\u5173\u4e8e(x-y)\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u5c31\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f\u4e86.
\u6307\u51fa\uff1a\u628a(x-y)\u770b\u4f5c\u4e00\u4e2a\u6574\u4f53\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u8fd9\u53c8\u662f\u8fd0\u7528\u4e86\u6570\u5b66\u4e2d\u7684\u201c\u6574\u4f53\u201d\u601d\u60f3\u65b9\u6cd5\u3002
\u4f8b5 x2+2x-15
\u5206\u6790\uff1a\u5e38\u6570\u9879(-15)<0\uff0c\u53ef\u5206\u89e3\u6210\u5f02\u53f7\u4e24\u6570\u7684\u79ef\uff0c\u53ef\u5206\u89e3\u4e3a(-1)(15)\uff0c\u6216(1)(-15)\u6216(3)
(-5)\u6216(-3)(5)\uff0c\u5176\u4e2d\u53ea\u6709(-3)(5)\u4e2d-3\u548c5\u7684\u548c\u4e3a2\u3002
=(x-3)(x+5)
\u603b\u7ed3\uff1a\u2460\u578b\u7684\u5f0f\u5b50\u7684\u56e0\u5f0f\u5206\u89e3
\u8fd9\u7c7b\u4e8c\u6b21\u4e09\u9879\u5f0f\u7684\u7279\u70b9\u662f\uff1a\u4e8c\u6b21\u9879\u7684\u7cfb\u6570\u662f1\uff1b\u5e38\u6570\u9879\u662f\u4e24\u4e2a\u6570\u7684\u79ef\uff1b\u4e00\u6b21\u9879\u7cfb\u6570\u662f\u5e38\u6570\u9879\u7684\u4e24\u4e2a\u56e0\u6570\u7684\u548c.\u56e0\u6b64\uff0c\u53ef\u4ee5\u76f4\u63a5\u5c06\u67d0\u4e9b\u4e8c\u6b21\u9879\u7684\u7cfb\u6570\u662f1\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\uff1a
\u2461kx2+mx+n\u578b\u7684\u5f0f\u5b50\u7684\u56e0\u5f0f\u5206\u89e3
\u5982\u679c\u80fd\u591f\u5206\u89e3\u6210k=ac\uff0cn=bd\uff0c\u4e14\u6709ad+bc=m \u65f6\uff0c\u90a3\u4e48
kx2+mx+n=(ax+b)(cx+d)
a b
\u2573
c d
1\uff0e\u76f4\u63a5\u5f00\u5e73\u65b9\u6cd5\uff1a
\u76f4\u63a5\u5f00\u5e73\u65b9\u6cd5\u5c31\u662f\u7528\u76f4\u63a5\u5f00\u5e73\u65b9\u6c42\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u65b9\u6cd5\u3002\u7528\u76f4\u63a5\u5f00\u5e73\u65b9\u6cd5\u89e3\u5f62\u5982\u7684
\u65b9\u7a0b\uff0c\u5176\u89e3\u4e3a.
\u4f8b1\uff0e\u89e3\u65b9\u7a0b\uff081\uff09(3x+1)2=7 \uff082\uff099x2-24x+16=11
\u5206\u6790\uff1a\uff081\uff09\u6b64\u65b9\u7a0b\u663e\u7136\u7528\u76f4\u63a5\u5f00\u5e73\u65b9\u6cd5\u597d\u505a\uff0c\uff082\uff09\u65b9\u7a0b\u5de6\u8fb9\u662f\u5b8c\u5168\u5e73\u65b9\u5f0f(3x-4)2\uff0c\u53f3\u8fb9=11>0\uff0c\u6240\u4ee5
\u6b64\u65b9\u7a0b\u4e5f\u53ef\u7528\u76f4\u63a5\u5f00\u5e73\u65b9\u6cd5\u89e3\u3002
\uff081\uff09\u89e3\uff1a(3x+1)2=7\u00d7
\u2234(3x+1)2=5
\u22343x+1=\u00b1(\u6ce8\u610f\u4e0d\u8981\u4e22\u89e3)
\u2234x=
\u2234\u539f\u65b9\u7a0b\u7684\u89e3\u4e3ax1=,x2=
\uff082\uff09\u89e3\uff1a 9x2-24x+16=11
\u2234(3x-4)2=11
\u22343x-4=\u00b1
\u2234x=
\u2234\u539f\u65b9\u7a0b\u7684\u89e3\u4e3ax1=,x2=
2\uff0e\u914d\u65b9\u6cd5\uff1a\u7528\u914d\u65b9\u6cd5\u89e3\u65b9\u7a0bax2+bx+c=0 (a\u22600)
\u5148\u5c06\u5e38\u6570c\u79fb\u5230\u65b9\u7a0b\u53f3\u8fb9\uff1aax2+bx=-c
\u5c06\u4e8c\u6b21\u9879\u7cfb\u6570\u5316\u4e3a1\uff1ax2+x=-
\u65b9\u7a0b\u4e24\u8fb9\u5206\u522b\u52a0\u4e0a\u4e00\u6b21\u9879\u7cfb\u6570\u7684\u4e00\u534a\u7684\u5e73\u65b9\uff1ax2+x+( )2=- +( )2
\u65b9\u7a0b\u5de6\u8fb9\u6210\u4e3a\u4e00\u4e2a\u5b8c\u5168\u5e73\u65b9\u5f0f\uff1a(x+ )2=
\u5f53b2-4ac\u22650\u65f6\uff0cx+ =\u00b1
\u2234x=(\u8fd9\u5c31\u662f\u6c42\u6839\u516c\u5f0f)
\u4f8b2\uff0e\u7528\u914d\u65b9\u6cd5\u89e3\u65b9\u7a0b 3x2-4x-2=0
\u89e3\uff1a\u5c06\u5e38\u6570\u9879\u79fb\u5230\u65b9\u7a0b\u53f3\u8fb9 3x2-4x=2
\u5c06\u4e8c\u6b21\u9879\u7cfb\u6570\u5316\u4e3a1\uff1ax2-x=
\u65b9\u7a0b\u4e24\u8fb9\u90fd\u52a0\u4e0a\u4e00\u6b21\u9879\u7cfb\u6570\u4e00\u534a\u7684\u5e73\u65b9\uff1ax2-x+( )2= +( )2
\u914d\u65b9\uff1a(x-)2=
\u76f4\u63a5\u5f00\u5e73\u65b9\u5f97\uff1ax-=\u00b1
\u2234x=
\u2234\u539f\u65b9\u7a0b\u7684\u89e3\u4e3ax1=,x2= .
3\uff0e\u516c\u5f0f\u6cd5\uff1a\u628a\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u5316\u6210\u4e00\u822c\u5f62\u5f0f\uff0c\u7136\u540e\u8ba1\u7b97\u5224\u522b\u5f0f\u25b3=b2-4ac\u7684\u503c\uff0c\u5f53b2-4ac<0\u65f6\uff0c\u65e0\u89e3\uff1b\u65b9\u7a0b\u5f53b2-4ac\u22650\u65f6\uff0c\u628a\u5404\u9879\u7cfb\u6570a, b, c\u7684\u503c\u4ee3\u5165\u6c42\u6839\u516c\u5f0f\u5c31\u53ef\u5f97\u5230\u65b9\u7a0b\u7684\u6839\u3002
\u4f8b3\uff0e\u7528\u516c\u5f0f\u6cd5\u89e3\u65b9\u7a0b2x2-8x=-5
\u89e3\uff1a\u5c06\u65b9\u7a0b\u5316\u4e3a\u4e00\u822c\u5f62\u5f0f\uff1a2x2-8x+5=0
\u2234a=2, b=-8, c=5
b2-4ac=(-8)2-4\u00d72\u00d75=64-40=24>0
\u2234x= = =
\u2234\u539f\u65b9\u7a0b\u7684\u89e3\u4e3ax1=,x2= .
4\uff0e\u56e0\u5f0f\u5206\u89e3\u6cd5\uff1a\u628a\u65b9\u7a0b\u53d8\u5f62\u4e3a\u4e00\u8fb9\u662f\u96f6\uff0c\u628a\u53e6\u4e00\u8fb9\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\u5206\u89e3\u6210\u4e24\u4e2a\u4e00\u6b21\u56e0\u5f0f\u7684\u79ef\u7684\u5f62\u5f0f\uff0c\u8ba9
\u4e24\u4e2a\u4e00\u6b21\u56e0\u5f0f\u5206\u522b\u7b49\u4e8e\u96f6\uff0c\u5f97\u5230\u4e24\u4e2a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\uff0c\u89e3\u8fd9\u4e24\u4e2a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u6240\u5f97\u5230\u7684\u6839\uff0c\u5c31\u662f\u539f\u65b9\u7a0b\u7684\u4e24\u4e2a\u6839\u3002\u8fd9\u79cd\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u7684\u65b9\u6cd5\u53eb\u505a\u56e0\u5f0f\u5206\u89e3\u6cd5\u3002
\u4f8b4\uff0e\u7528\u56e0\u5f0f\u5206\u89e3\u6cd5\u89e3\u4e0b\u5217\u65b9\u7a0b\uff1a
(1) (x+3)(x-6)=-8 (2) 2x2+3x=0
(3) 6x2+5x-50=0 (\u9009\u5b66\uff09 (4)x2-2( + )x+4=0 \uff08\u9009\u5b66\uff09
(1)\u89e3\uff1a(x+3)(x-6)=-8 \u5316\u7b80\u6574\u7406\u5f97
x2-3x-10=0 (\u65b9\u7a0b\u5de6\u8fb9\u4e3a\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u53f3\u8fb9\u4e3a\u96f6)
(x-5)(x+2)=0 (\u65b9\u7a0b\u5de6\u8fb9\u5206\u89e3\u56e0\u5f0f)
\u2234x-5=0\u6216x+2=0 (\u8f6c\u5316\u6210\u4e24\u4e2a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b)
\u2234x1=5,x2=-2\u662f\u539f\u65b9\u7a0b\u7684\u89e3\u3002
(2)\u89e3\uff1a2x2+3x=0
x(2x+3)=0 (\u7528\u63d0\u516c\u56e0\u5f0f\u6cd5\u5c06\u65b9\u7a0b\u5de6\u8fb9\u5206\u89e3\u56e0\u5f0f)
\u2234x=0\u62162x+3=0 (\u8f6c\u5316\u6210\u4e24\u4e2a\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b)
\u2234x1=0\uff0cx2=-\u662f\u539f\u65b9\u7a0b\u7684\u89e3\u3002
\u6ce8\u610f\uff1a\u6709\u4e9b\u540c\u5b66\u505a\u8fd9\u79cd\u9898\u76ee\u65f6\u5bb9\u6613\u4e22\u6389x=0\u8fd9\u4e2a\u89e3\uff0c\u5e94\u8bb0\u4f4f\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u6709\u4e24\u4e2a\u89e3\u3002
(3)\u89e3\uff1a6x2+5x-50=0
(2x-5)(3x+10)=0 (\u5341\u5b57\u76f8\u4e58\u5206\u89e3\u56e0\u5f0f\u65f6\u8981\u7279\u522b\u6ce8\u610f\u7b26\u53f7\u4e0d\u8981\u51fa\u9519)
\u22342x-5=0\u62163x+10=0
\u2234x1=, x2=- \u662f\u539f\u65b9\u7a0b\u7684\u89e3\u3002
(4)\u89e3\uff1ax2-2(+ )x+4 =0 \uff08\u22354 \u53ef\u5206\u89e3\u4e3a2 \u00b72 \uff0c\u2234\u6b64\u9898\u53ef\u7528\u56e0\u5f0f\u5206\u89e3\u6cd5\uff09
(x-2)(x-2 )=0
\u2234x1=2 ,x2=2\u662f\u539f\u65b9\u7a0b\u7684\u89e3\u3002
\u4e8c\u5143\u4e8c\u6b21\u65b9\u7a0b\uff1a\u542b\u6709\u4e24\u4e2a\u672a\u77e5\u6570\u4e14\u672a\u77e5\u6570\u7684\u6700\u9ad8\u6b21\u6570\u4e3a2\u7684\u6574\u5f0f\u65b9\u7a0b\u3002
10\u4e09\u5143\u4e00\u6b21\u65b9\u7a0b
\u7f16\u8f91
\u5b9a\u4e49
\u4e0e\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7c7b\u4f3c\uff0c\u4e09\u4e2a\u7ed3\u5408\u5728\u4e00\u8d77\u7684\u5171\u542b\u6709\u4e09\u4e2a\u672a\u77e5\u6570\u7684\u4e00\u6b21\u65b9\u7a0b\u3002
\u89e3\u6cd5
\u4e0e\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7c7b\u4f3c\uff0c\u5229\u7528\u6d88\u5143\u6cd5\u9010\u6b65\u6d88\u5143\u3002
\u5178\u578b\u9898\u6790
\u67d0\u5730\u533a\u4e3a\u4e86\u9f13\u52b1\u8282\u7ea6\u7528\u6c34,\u5bf9\u81ea\u6765\u6c34\u7684\u6536\u8d39\u6807\u51c6\u4f5c\u5982\u4e0b\u89c4\u5b9a\uff1a\u6bcf\u6708\u6bcf\u6237\u7528\u6c34\u4e0d\u8d85\u8fc710\u5428\u63090.9\u5143/\u5428\u6536\u8d39;\u8d85\u8fc710\u5428\u800c\u4e0d\u8d85\u8fc720\u5428\u63091.6\u5143/\u5428\u6536\u8d39;\u8d85\u8fc720\u5428\u7684\u90e8\u5206\u63092.4\u5143/\u5428\u6536\u8d39\u3002\u67d0\u6708\u7532\u7528\u6237\u6bd4\u4e59\u7528\u6237\u591a\u7f34\u6c34\u8d3916\u5143\uff0c\u4e59\u7528\u6237\u6bd4\u4e19\u7528\u6237\u591a\u7f34\u6c34\u8d397.5\u5143\u3002\u5df2\u77e5\u4e19\u7528\u6237\u7528\u6c34\u4e0d\u523010\u5428,\u4e59\u7528\u6237\u7528\u6c34\u8d85\u8fc710\u5428\u4f46\u4e0d\u523020\u5428.\u95ee:\u7532\u3002\u4e59.\u4e19\u4e09\u7528\u6237\u8be5\u6708\u5404\u7f34\u6c34\u8d39\u591a\u5c11\u5143(\u6309\u6574\u5428\u8ba1\u7b97\u6536\u8d39)?
\u89e3\uff1a\u8bbe\u7532\u7528\u6c34x\u5428\uff0c\u4e59\u7528\u6c34y\u5428\uff0c\u4e19\u7528\u6c34z\u5428
\u663e\u7136\uff0c\u7532\u7528\u6237\u7528\u6c34\u8d85\u8fc7\u4e8620\u5428
\u6545\u7532\u7f34\u8d39\uff1a0.9*10+1.6*10+2.4*(x-20)=2.4x-23
\u4e59\u7f34\u8d39\uff1a0.9*10+1.6*(y-10)=1.6y-9
\u4e19\u7f34\u8d39\uff1a0.9z
2.4x-23=1.6y-7+16
1.6y-7=0.9z+7.5
\u5316\u7b80\u5f97
3x-2y=40\u2026\u2026(1)
16y-9z=145\u2026\u2026(2)
\u7531(1)\u5f97x=(2y+40)/3
\u6240\u4ee5\u8bbey=1+3k,3<k<7
\u5f53k=4,y=13,x=22,\u4ee3\u5165(2)\u6c42\u5f97z=7
\u5f53k=5,y=16,\u4ee3\u5165(2),z\u6ca1\u6574\u6570\u89e3
\u5f53k=6,y=19,\u4ee3\u5165(2),z\u6ca1\u6574\u6570\u89e3
\u6240\u4ee5\u7532\u7528\u6c3422\u5428\uff0c\u4e59\u7528\u6c3413\u5428\uff0c\u4e19\u7528\u6c347\u5428
\u7532\u7528\u6c3429.8\u5143,\u4e59\u7528\u6c3413.8\u5143\uff0c\u4e19\u7528\u6c346.3\u5143
11\u591a\u5143\u4e00\u6b21\u65b9\u7a0b
\u7f16\u8f91
\u6d88\u5143\u6cd5
\u8bbe\u65b9\u7a0b\u7ec4\u2460\uff1a
\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026
\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026
\u628a\u65b9\u7a0b(1)\u00d7(-i1/a1)\u52a0\u5230\uff08i\uff09\u4e0a\uff0c\u518d\u628a\u65b9\u7a0b(2)\u00d7(-i2/a2)\u52a0\u5230\uff08i\uff09\u4e0a\uff0c\u4ee5\u6b64\u7c7b\u63a8\u3002(i\u2208N\u4e14i\u2208[1\uff0cm])\u6700\u540e\uff0c\u65b9\u7a0b\u7ec4\u53d8\u4e3a\uff1a\u2461
b11 x1+b12 x2+b13 x3+\u2026+b1n xn=c1
b22 x2+b13 x3+\u2026+b2n xn=c2
\u2026\u2026\u2026\u2026\u2026\u2026
brn xn=cr
0=cr+1
0=0
0=0
\u2026\u2026\u2026\u2026 (bii\u22600,i=1,2,\u2026r)
\u6700\u540e\u7684\u8bb8\u591a0=0\u53ef\u4ee5\u820d\u53bb\uff0c\u4e0d\u5f71\u54cd\u65b9\u7a0b\u7684\u89e3\u3002\u53ef\u4ee5\u5206\u4e09\u79cd\u60c5\u51b5\uff1a
\uff081\uff09cr+1 \u22600
\u6b64\u65f6\uff0c\u6ee1\u8db3\u524dr\u5404\u65b9\u7a0b\u7684\u4efb\u610f\u4e00\u4e2a\u89e3\uff0c\u90fd\u4e0d\u80fd\u6ee1\u8db30=cr+1\u8fd9\u4e2a\u65b9\u7a0b\uff0c\u6240\u4ee5\u2461\u65e0\u89e3\uff0c\u6240\u4ee5\u2460\u4e5f\u65e0\u89e3
\u5f53cr+1=0\u65f6\uff0c\u53c8\u5206\u4e24\u79cd\u60c5\u51b5\uff1a
\uff082\uff09r=n
\u56e0\u4e3abii\u22600,\u6240\u4ee5\u4ece\u6700\u540e\u4e00\u4e2a\u65b9\u7a0b\u53ef\u89e3\u51faxn\u3002\u7136\u540e\u4ee3\u5165\u7b2cr-1\u4e2a\u65b9\u7a0b,\u89e3\u51faxn-1\u3002\u5982\u6b64\u7c7b\u63a8\uff0c\u53ef\u5f97\u51fa\u65b9\u7a0b\u7ec4\u2461\u7684\u552f\u4e00\u89e3\uff0c\u5c31\u662f\u65b9\u7a0b\u7ec4\u2460\u7684\u552f\u4e00\u89e3\u3002
\uff083)r<n
\u53ef\u628a\u65b9\u7a0b\u7ec4\u8be5\u6210\u4ed6\u7684\u540c\u89e3\u65b9\u7a0b\u7ec4\u2462\uff1a
b11 x1+b12 x2+b13 x3+\u2026+b1r xr=c1-b1,r+1 xr+1-\u2026-b1n xn
b22 x2+b13 x3+\u2026+b2n xr=c2-b2,r+1 xr+1-\u2026-b2n xn
\u2026\u2026\u2026\u2026\u2026\u2026
brr xr=cr-br,r+1 xr+1-\u2026-brn xn
\u8bbe\u7b49\u53f7\u540e\u9762\u7684\u6570\u662f\u5df2\u77e5\u6570\uff0c\u6309\u7167\uff082\uff09\u7684\u65b9\u6cd5\u6765\u89e3\uff0c\u53ef\u89e3\u5f97\uff1a
x1=d11 xr+1+d12 xr+2+\u2026+d1,n-r xn
x2=d21 xr+1+d22 xr+2+\u2026+d1,n-r xn
\u2026\u2026\u2026\u2026\u2026\u2026
xr=dr1 xr+1+dr2 xr+2+\u2026+dr,n-r xn
\u4ee4\u81ea\u7531\u672a\u77e5\u91cfxr+i=ki(i\u2208N\u4e14i\u2208[1\uff0cn-r])\u53ef\u5f97\u65b9\u7a0b\u7ec4\u7684\u5168\u90e8\u89e3\uff1a
x1=d11 k1+d12 k2+\u2026+ d1,n-r kn-r
x2=d21 k1+d22 k2+\u2026+d1,n-r kn-r
\u2026\u2026\u2026\u2026\u2026\u2026
xr=dr1 k1+dr2 k2+\u2026+dr,n-r kn-r
xr+1=k1
xr+2=k2
\u2026\u2026\u2026\u2026
xn=kn-r
\u5176\u4ed6\u89e3\u6cd5
\u514b\u83b1\u59c6\u6cd5\u5219
\uff08\u6b64\u6cd5\u53ea\u9002\u7528\u4e8em=n\u4e14D\u22600\u7684\u65b9\u7a0b\u7ec4\uff09
\u8bbe\u7cfb\u6570\u884c\u5217\u5f0fD=\u2223a ij\u2223,Di\u662fD\u628ai\u5217\u6362\u6210\u7ed3\u679c\u7684\u884c\u5217\u5f0f
\u90a3\u4e48xi=Di/D(i\u2208N\u4e14i\u2208[1\uff0cn])
\u77e9\u9635\u548c\u5411\u91cf\u89e3\u6cd5
\u77e9\u9635\u89e3\u6cd5\u5373\u628a\u65b9\u7a0b\u7ec4\u2460\u7684\u589e\u5e7f\u77e9\u9635\u8fdb\u884c\u521d\u7b49\u884c\u53d8\u5316\u3002
\u5411\u91cf\u89e3\u6cd5\u5373\u628a\u65b9\u7a0b\u7ec4\u2460\u6539\u5199\u6210Ax=b\u7684\u5f62\u5f0f\u3002
\u5148\u6c42\u51fa\u65b9\u7a0b\u7ec4\u7684\u7279\u89e3\u03b7\uff0c\u7136\u540e\u6c42\u5176\u5bf9\u5e94\u5bfc\u51fa\u7ec4Ax=0\u7684\u89e3\u03be1\uff0c\u03be2\uff0c\u2026\uff0c\u03ben\u3002
\u65b9\u7a0b\u7ec4\u7684\u89e3\u4e3a\uff1a\u03b7+c1\u03be1+c2\u03be2+\u2026+cn\u03ben\u3002
12\u76f4\u7ebf\u65b9\u7a0b
\u7f16\u8f91
(1)\u4e00\u822c\u5f0f\uff1a Ax+By+C=0 (\u5176\u4e2dA\u3001B\u4e0d\u540c\u65f6\u4e3a0) \u9002\u7528\u4e8e\u6240\u6709\u76f4\u7ebf
\u76f4\u7ebfl1\uff1aA1x+B1y+C1=0
\u76f4\u7ebfl2\uff1aA2x+B2y+C2=0
\u4e24\u76f4\u7ebf\u5e73\u884c\u65f6\uff1aA1/A2=B1/B2\u2260C1/C2
\u4e24\u76f4\u7ebf\u5782\u76f4\u65f6\uff1aA1A2+B1B2=0
\u4e24\u76f4\u7ebf\u91cd\u5408\u65f6\uff1aA1/A2=B1/B2=C1/C2
\u4e24\u76f4\u7ebf\u76f8\u4ea4\u65f6\uff1aA1/A2\u2260B1/B2
(2)\u70b9\u659c\u5f0f\uff1a \u77e5\u9053\u76f4\u7ebf\u4e0a\u4e00\u70b9(x0,y0),\u5e76\u4e14\u76f4\u7ebf\u7684\u659c\u7387k\u5b58\u5728\uff0c\u5219\u76f4\u7ebf\u53ef\u8868\u793a\u4e3a y-y0=k(x-x0)\u3002\u5f53k\u4e0d\u5b58\u5728\u65f6\uff0c\u76f4\u7ebf\u53ef\u8868\u793a\u4e3a x=x0
(3)\u622a\u8ddd\u5f0f\uff1a \u82e5\u76f4\u7ebf\u4e0ex\u8f74\u4ea4\u4e8e(a,0),\u4e0ey\u8f74\u4ea4\u4e8e(0,b),\u5219\u76f4\u7ebf\u53ef\u8868\u793a\u4e3a\uff1ax/a+y/b=1\u3002\u6240\u4ee5\u4e0d\u9002\u7528\u4e8e\u548c\u4efb\u610f\u5750\u6807\u8f74\u5782\u76f4\u7684\u76f4\u7ebf\u548c\u8fc7\u539f\u70b9\u7684\u76f4\u7ebf \u3002
(4)\u659c\u622a\u5f0f\uff1a y=kx+b (k\u22600)
(5)\u4e24\u70b9\u5f0f\uff1a\u82e5\u76f4\u7ebf\u8fc7\u4efb\u610f\u4e24\u70b9(x1,y1)\u3001(x2,y2)\uff0c\u4e14 x1\u2260x2,y1\u2260y2\uff0c\u5219\u76f4\u7ebf\u53ef\u4ee5\u8868\u793a\u4e3a
(6)\u6cd5\u7ebf\u5f0f\uff1a x\u00b7cos\u03b1+ysin\u03b1-p=0
13\u9644\u6ce8
\u7f16\u8f91
\u4e00\u822c\u5730\uff0cn\u5143\u4e00\u6b21\u65b9\u7a0b\u5c31\u662f\u542b\u6709n\u4e2a\u672a\u77e5\u6570\uff0c\u4e14\u542b\u672a\u77e5\u6570\u9879\u6b21\u6570\u662f1\u7684\u65b9\u7a0b\uff0c\u4e00\u6b21\u9879\u7cfb\u6570\u89c4\u5b9a\u4e0d\u7b49\u4e8e0
n\u5143\u4e00\u6b21\u65b9\u7a0b\u7ec4\u5c31\u662f\u51e0\u4e2an\u5143\u4e00\u6b21\u65b9\u7a0b\u7ec4\u6210\u7684\u65b9\u7a0b\u7ec4\uff08\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u9664\u5916\uff09
\u4e00\u5143a\u6b21\u65b9\u7a0b\u5c31\u662f\u542b\u6709\u4e00\u4e2a\u672a\u77e5\u6570\uff0c\u4e14\u542b\u672a\u77e5\u6570\u9879\u6700\u9ad8\u6b21\u6570\u662fa\u7684\u65b9\u7a0b\uff08\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u9664\u5916\uff09
\u4e00\u5143a\u6b21\u65b9\u7a0b\u7ec4\u5c31\u662f\u51e0\u4e2a\u4e00\u5143a\u6b21\u65b9\u7a0b\u7ec4\u6210\u7684\u65b9\u7a0b\u7ec4\uff08\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u9664\u5916\uff09
n\u5143a\u6b21\u65b9\u7a0b\u5c31\u662f\u542b\u6709n\u4e2a\u672a\u77e5\u6570\uff0c\u4e14\u542b\u672a\u77e5\u6570\u9879\u6700\u9ad8\u6b21\u6570\u662fa\u7684\u65b9\u7a0b\uff08\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u9664\u5916\uff09
n\u5143a\u6b21\u65b9\u7a0b\u7ec4\u5c31\u662f\u51e0\u4e2an\u5143a\u6b21\u65b9\u7a0b\u7ec4\u6210\u7684\u65b9\u7a0b\u7ec4\uff08\u4e00\u5143\u4e00\u6b21\u65b9\u7a0b\u9664\u5916\uff09
\u65b9\u7a0b\uff08\u7ec4\uff09\u4e2d\uff0c\u672a\u77e5\u6570\u4e2a\u6570\u5927\u4e8e\u65b9\u7a0b\u4e2a\u6570\u7684\u65b9\u7a0b\uff08\u7ec4\uff09\u53eb\u505a\u4e0d\u5b9a\u65b9\u7a0b\uff08\u7ec4\uff09\uff0c\u6b64\u7c7b\u65b9\u7a0b\uff08\u7ec4\uff09\u4e00\u822c\u6709\u65e0\u6570\u4e2a\u89e3\u3002
14\u9e21\u5154\u540c\u7b3c\u95ee\u9898
\u7f16\u8f91
\u89e3\u6cd5\u516c\u5f0f
\u89e3\u6cd51\uff1a\uff08\u5154\u7684\u811a\u6570\u00d7\u603b\u53ea\u6570\uff0d\u603b\u811a\u6570\uff09\u00f7\uff08\u5154\u7684\u811a\u6570\uff0d\u9e21\u7684\u811a\u6570\uff09=\u9e21\u7684\u53ea\u6570
\u603b\u53ea\u6570\uff0d\u9e21\u7684\u53ea\u6570=\u5154\u7684\u53ea\u6570
\u89e3\u6cd52\uff1a\uff08 \u603b\u811a\u6570\uff0d\u9e21\u7684\u811a\u6570\u00d7\u603b\u53ea\u6570\uff09\u00f7\uff08\u5154\u7684\u811a\u6570\uff0d\u9e21\u7684\u811a\u6570\uff09 =\u5154\u7684\u53ea\u6570
\u603b\u53ea\u6570\uff0d\u5154\u7684\u53ea\u6570=\u9e21\u7684\u53ea\u6570
\u89e3\u6cd53\uff1a\u603b\u811a\u6570\u00f72\u2014\u603b\u5934\u6570=\u5154\u7684\u53ea\u6570
\u603b\u53ea\u6570\u2014\u5154\u7684\u53ea\u6570=\u9e21\u7684\u53ea\u6570
\u89e3\u6cd54\uff08\u65b9\u7a0b\uff09\uff1aX=\u603b\u811a\u6570\u00f72\u2014\u603b\u5934\u6570\uff08X=\u5154\u7684\u53ea\u6570\uff09
\u603b\u53ea\u6570\u2014\u5154\u7684\u53ea\u6570=\u9e21\u7684\u53ea\u6570
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15\u65b9\u7a0b\u5206\u7c7b
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2\u4e2a\u4ee5\u4e0a\uff08\u5076\u6570\u4e2a\uff09
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计算器是操作不了这种形式的，只能计算一些运算而不是只能计算。
得自己化解后根据加减乘除运算
用Alpha输入等号（键盘上半的函数区左上角，Alpha下面的那个），然后Shift，Solve（函数区第一个），猜测一个值，按=，等一会儿就会出结果
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用的是专业计算器吗？
如果是 照着输入进去就OK了
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