数学研究：x，y，z为正整数，且x的平方加上y的平方加上z的平方等于44100，那么x，y，z是多少？ x的平方+y的平方=z的平方 如何快速求出答案？
\u5df2\u77e5x y z\u5747\u4e3a\u6b63\u6574\u6570 \u4e14\u6ee1\u8db3x\u7684\u5e73\u65b9\uff0bz\u7684\u5e73\u65b9=10\uff0cz\u7684\u5e73\u65b9+y\u7684\u5e73\u65b9=13,\u6c42\uff08x-y)\u7684x² + z² = 10
y² + z² = 13
\u7b49\u5f0f\u76f8\u51cf\u5f97\u5230x² - y² = -3\uff0c\u8fd9\u5c31\u8bf4\u660e x<y
\u9898\u76ee\u5df2\u77e5\u4e86x,y,z\u5747\u4e3a\u6b63\u6574\u6570
\u8fd9\u65f6\u5019\u6211\u4eec\u901a\u8fc7x² + z² = 10\u6211\u4eec\u5f97\u5230x\uff0cz\u5fc5\u7136\u90fd\u5c0f\u4e8e\u7b49\u4e8e3\uff0c\u5e76\u4e14\u53d6\u503c\u53ea\u53ef\u80fd\u662f1,3\uff08x = 1\uff0cz =3\u6216\u8005x = 3\uff0cz =1\uff09
\u6211\u4eec\u901a\u8fc7y² + z² = 13\u6211\u4eec\u5f97\u5230y\uff0cz\u5fc5\u7136\u90fd\u5c0f\u4e8e\u7b49\u4e8e3\uff0c\u5e76\u4e14\u53d6\u503c\u53ea\u53ef\u80fd\u662f2,3\uff08y = 2\uff0cz =3\u6216\u8005y = 3\uff0cz =2\uff09
\u7ed3\u5408x<y\u4ee5\u53cax² - y² = -3\u6211\u4eec\u5f97\u5230\uff0c\u5fc5\u7136x = 1\uff0cy=2
\u6240\u4ee5\u7b54\u6848\u51fa\u6765\u4e86\uff0c\u4eb2\uff0c\u7ed9\u597d\u8bc4\u5965
1\uff0e \u5b9a\u4e49\uff1a\u51e1\u7b26\u5408X\uff3e2+Y\uff3e2=Z\uff3e2\u516c\u5f0f\u7684\u6b63\u6574\u6570\u503c\u6211\u4eec\u79f0\u4e4b\u4e3a\u52fe\u80a1\u6570\u3002
2\uff0e \u51e1\u6709\u516c\u7ea6\u6570\u7684\u52fe\u80a1\u6570\u6211\u4eec\u79f0\u4e4b\u4e3a\u6d3e\u751f\u52fe\u80a1\u6570\uff0c\u4f8b[30\uff0c40\uff0c50] \u7b49\uff1b
3\uff0e \u65e0\u516c\u7ea6\u6570\u7684\u52fe\u80a1\u6570\uff0c\u4f8b[3\uff0c4\uff0c5]\uff1b[8\uff0c15\uff0c17]\u7b49\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u52fe\u80a1\u6570\u3002\u5168\u662f\u5076\u6570\u7684\u52fe\u80a1\u6570\u5fc5\u662f\u6d3e\u751f\u52fe\u80a1\u6570\uff0c\u4e09\u4e2a\u5947\u6570\u4e0d\u53ef\u80fd\u7b26\u5408\u5b9a\u4e49\u516c\u5f0f\u3002\u56e0\u6b64\uff0c\u52fe\u80a1\u6570\u552f\u4e00\u7684\u53ef\u80fd\u6027\u662f\uff1a
X\u548cY\u5206\u522b\u662f\u5947\u6570\u548c\u5076\u6570\uff08\u5076\u6570\u548c\u5947\u6570\uff09\uff0c\u659c\u8fb9Z\u53ea\u80fd\u662f\u5947\u6570\u3002
4\uff0e \u52fe\u80a1\u6570\u5177\u6709\u4ee5\u4e0b\u7279\u6027\uff1a
\u659c\u8fb9\u4e0e\u5076\u6570\u8fb9\u4e4b\u5dee\u662f\u5947\u6570,\u8fd9\u4e2a\u5947\u6570\u53ea\u80fd\u662f\u67d0\u5947\u6570\u7684\u5e73\u65b9\u6570, \u4f8b1,9,25,49,\u2026\u2026\uff0c\u81f3\u65e0\u7a77\u5927\uff1b
\u659c\u8fb9\u4e0e\u5947\u6570\u8fb9\u4e4b\u5dee\u662f\u5076\u6570,\u8fd9\u4e2a\u5076\u6570\u53ea\u80fd\u662f\u67d0\u5076\u6570\u5e73\u65b9\u6570\u7684\u4e00\u534a, \u4f8b2\uff0c8\uff0c18\uff0c32\uff0c\u2026\u2026\uff0c\u81f3\u65e0\u7a77\u5927\uff1b
5\uff0e \u7531\u4ee5\u4e0a\u5b9a\u4e49\u6211\u4eec\u63a8\u5bfc\u51fa\u52fe\u80a1\u516c\u5f0f\uff1a
X = P\uff3e2 + PQ\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\uff08X\u7b49\u4e8eP\u5e73\u65b9\u52a0PQ\uff09
Y = Q\uff3e2/ 2 + PQ\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\uff08Y\u7b49\u4e8e\u4e8c\u5206\u4e4bQ\u65b9\u52a0PQ\uff09
Z = P\uff3e2 + Q\uff3e2 / 2 + PQ\u3000\u3000\u3000\u3000\uff08Z\u7b49\u4e8eP\u5e73\u65b9\u52a0\u4e8c\u5206\u4e4bQ\u65b9\u52a0PQ\uff09
6\uff0e \u6b64\u516c\u5f0f\u6db5\u76d6\u4e86\u81ea\u7136\u754c\u7684\u5168\u90e8\u52fe\u80a1\u6570\uff0c\u5305\u62ec\u6d3e\u751f\u52fe\u80a1\u6570\u3002
7\uff0e \u7528\u6b64\u516c\u5f0f\u5f88\u5bb9\u6613\u5bfc\u51fa\u5168\u90e8\u52fe\u80a1\u6570\uff0c\u4f8b\u59822000\u4ee5\u5185\u7684\u52fe\u80a1\u6570\u8ba1\u6709320\u7ec4,\uff08\u4e0d\u542b\u6d3e\u751f\u52fe\u80a1\u6570\uff09\u3002\u6700\u5927\u7684\u4e00\u7ec4\u662f [315, 1972, 1997]
8\uff0e \u659c\u8fb9\u662f1105\u548c1885\u7684\u52fe\u80a1\u6570\u5404\u67094\u7ec4\uff1a\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000\u3000
\u3000[47\uff0c1104\uff0c1105] [264\uff0c1703\uff0c1105] [576\uff0c943\uff0c1105] [744\uff0c817\uff0c1105]\uff1b
[427\uff0c1836\uff0c1885] [1003\uff0c1596\uff0c1885] [1643\uff0c924\uff0c1885] [1813\uff0c516\uff0c1885]\uff1b
9\uff0e \u4ee5\u4efb\u610f\u5947\u6570\u4ee3\u5165P \uff0c\u4efb\u610f\u5076\u6570\u4ee3\u5165Q \uff0c\u5373\u53ef\u5f97\u5230\u552f\u4e00\u4e00\u7ec4\u52fe\u80a1\u6570\u3002
\u4f8b\u5982P = 5 \uff0cQ = 8 \uff0c\u5f97\u5230
X = 25 + 5\u00d78 = 65
Y = 32 + 5\u00d78 = 72
Z = 25 + 32 + 5\u00d78 = 97
10\uff0e \u5b83\u6781\u6e05\u695a\u5730\u663e\u793a\u51fa\u4e86\u659c\u8fb9\u4e0e\u5076\u6570\u76f4\u89d2\u8fb9\u4e4b\u5dee\u662f\u5947\u6570\u7684\u5e73\u65b9\uff0c\u659c\u8fb9\u4e0e\u5947\u6570\u76f4\u89d2\u8fb9\u4e4b\u5dee\u662f\u5076\u6570\u5e73\u65b9\u503c\u7684\u4e00\u534a\uff0c\u800c\u659c\u8fb9\u5219\u662f\u7531\u5947\u6570\u7684\u5e73\u65b9\u4e0e\u5076\u6570\u5e73\u65b9\u7684\u4e00\u534a\u548c\u6b64\u5947\u6570\u4e0e\u5076\u6570\u4e4b\u79ef\u4e09\u9879\u4e4b\u548c\u6240\u6784\u6210\u3002
11\uff0e \u5f53P\u4e0eQ\u6709\u516c\u7ea6\u6570\u65f6\uff0c\u4f8b\u59829\u4e0e12 \uff0c\u518d\u4f8b\u598221\u4e0e28\u7b49\uff0c\u63a8\u5bfc\u51fa\u6765\u7684\u662f\u6d3e\u751f\u52fe\u80a1\u6570\uff1b
\u5f53P\u4e0eQ\u65e0\u516c\u7ea6\u6570\u65f6\uff0c\u4f8b\u59829 \u4e0e8 \uff0c\u518d\u4f8b\u598221\u4e0e16\u7b49\uff0c\u63a8\u5bfc\u51fa\u6765\u7684\u662f\u52fe\u80a1\u6570\uff1b
12\uff0e \u4e0d\u5b58\u5728\u4e0d\u7b26\u5408\u672c\u516c\u5f0f\u7684\u52fe\u80a1\u6570\u3002\u4f8b\u5982\u6709\u4eba\u5949\u732e\u8da3\u5473\u52fe\u80a1\u6570[88209\uff0c90288\uff0c126225]\uff0c\u5b83\u5b9e\u9645 \u662f\u4e2a\u6d3e\u751f\u52fe\u80a1\u6570\uff0c\u5b83\u662f[297\uff0c304\uff0c425]\u4e58297\u500d\u800c\u6210\uff0c\u5b83\u662f\u7531P = 11\u548cQ = 16\u5bfc\u51fa\u3002
13\uff0e \u672c\u6587\u6240\u63d0\u4f9b\u7684\u516c\u5f0f\u662f\u4f9d\u636e\u672c\u6587\u7b2c4\u6761\u7684\u4e24\u6761\u52fe\u80a1\u6570\u7279\u6027\u89c4\u5f8b\u63a8\u5bfc\u800c\u51fa\uff0c\u4f46\u662f\u5b83\u53ef\u4ee5\u4e0e\u516d\u767e\u5e74\u524d\u5370\u5ea6\u5a46\u7f57\u95e8\u7b08\u591a\u516c\u5f0f\u76f8\u4e92\u63a8\u5bfc\u3002
14\uff0e \u4f9d\u636e\u672c\u516c\u5f0f\u52fe\u80a1\u5b9a\u7406\u53ef\u4ece\u6b63\u6574\u6570\u62d3\u5c55\u5230\u8d1f\u6574\u6570\u3002\u5728\u7b1b\u5361\u5c14\u5ea7\u6807\u56fe\u4e0a\uff0c\u52fe\u80a1\u4e09\u89d2\u5f62\u53ef\u4ee5\u5728\u66f4\u5927\u7684\u4f4d\u7f6e\u4e0a\u663e\u73b0\u3002
\u4e0d\u77e5\u9053\u4f60\u80fd\u4e0d\u80fd\u770b\u61c2\u3002
200,50,40
40000+2500+1600=44100
他们一定不是连续的数50,200,40
最小公倍数是10吧
用秦九昭 算术法,这是高二的内容
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