《九章算术》“勾股”章有一题：“仅有户高多于六尺八寸，两隔去适一丈。问户高、广各几何。” 今有户高多于广六尺八寸，两隅相去适一丈。问户高、广各几何？
\u300a\u4e5d\u7ae0\u7b97\u672f\u300b\u201c\u52fe\u80a1\u201d\u7ae0\u6709\u4e00\u9898\uff1a\u201c\u4ec5\u6709\u6237\u9ad8\u591a\u4e8e\u516d\u5c3a\u516b\u5bf8\uff0c\u4e24\u9694\u53bb\u9002\u4e00\u4e08\u3002\u95ee\u6237\u9ad8\u3001\u5e7f\u5404\u51e0\u4f55\u3002\u201d\u6362\u7b97\u7b49\u5f0f\u5e94\u8be5\u662f10\u5bf8\uff1d1\u5c3a\uff0c\u5341\u5c3a\uff1d\u4e00\u4e08\uff0c\u90a3\u4e48\u516d\u5c3a\u516b\u5bf8\u5c31\u662f0.68\u4e08\u4e86\uff0c\u8bbe\u5bf9\u89d2\u7ebf\u5bf9\u7740\u7684\u89d2\u662f\u89d2C\uff0c\u9ad8\u4e3ax\u4e08\uff0c\u5219\u5bbd\u4e3a\uff08x\uff0d0.68\uff09\u4e08\uff0c\u5229\u7528\u4f59\u5f26\u5b9a\u7406c*c=a*a+b*b-2ab*cos C\uff0c\uff08*\u662f\u4e58\u53f7\uff09\u53ef\u4ee5\u5217\u51fa\u65b9\u7a0b\u6709
1\uff1dx*x\uff0bx*x\uff0d1.36x\uff0b0.68*0.68-2*x*\uff08x-0.68\uff09cosC\uff0c
\u56e0\u4e3a\u5bf9\u89d2\u7ebf\u5bf9\u7740\u7684C\u89d2\u662f90\u5ea6\uff0c\u5219cosC\uff1d0\uff0c\u4e8e\u662f\u6709
1=2*x*x-1.36x\uff0b0.4624\uff0c\u7ed3\u679c\u6709\u4e24\u4e2a\uff0c\u820d\u53bb\u4e3a\u8d1f\u6570\u7684\u90a3\u4e2a\u5373\u53ef\u3002
\u89e3\uff1a\u8bbe\u5bbd\u4e3ax\u5c3a\uff0c\u5219\u9ad8\u4e3a\uff08x 6.8\uff09\u5c3a
\u7531\u9898\u610f\u5f97x2 \uff08x 6.8\uff092=102
\u89e3\u5f97x1=-9.6\uff08\u820d\u53bb\uff09\uff0cx2=2.8\uff08\u5c3a\uff09\uff0c
\u2234 \u5bbd\u4e3a2.8\u5c3a\uff0c\u9ad8\u4e3a9.6\u5c3a\u3002
则x²+(x+6.8)²=10²
2x²+13.6x-53.76=0
∴利用求根公式可知:x=2.8
x+6.8=9.6
所以门宽2尺8寸,高9尺6寸
假设宽为X，则长是X+0.68（丈），所以:X∧2+(X+0.68)∧2=1∧2。化简得：
2X∧2+1.36X-0.5376=0
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绛旓細瑙:璁鹃棬瀹戒负x灏,鍒欓珮涓簒+6.8灏 鍒檟²+(x+6.8)²=10²2x²+13.6x-53.76=0 鈭村埄鐢ㄦ眰鏍瑰叕寮忓彲鐭:x=2.8 x+6.8=9.6 鎵浠ラ棬瀹2灏8瀵,楂9灏6瀵
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