证明√X2+Y2+√(X-1)2+Y2+√X2+(Y-1)2+√(X-1)2+(Y-1)2>=2√2并求=成立时X与Y的

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/19 04:55:09

证明√X2+Y2+√(X-1)2+Y2+√X2+(Y-1)2+√(X-1)2+(Y-1)2>=2√2并求=成立时X与Y的值

√X2+Y2+√(X-1)2+Y2+√X2+(Y-1)2+√(X-1)2+(Y-1)2>=2√2
在\x\=\y\,\x-1\=y,\y-1\=\x\,\x-1\=\y-1\时值最小
解得x=1/2,y=1/2
代入原式:
√X2+Y2+√(X-1)2+Y2+√X2+(Y-1)2+√(X-1)2+(Y-1)2
=4根号(1/2)
=2根号2
所以x=1/2,y=1/2

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