Question

已知x2+y2-10x-6y+34=0,求（x-y/x+y）2÷x2-y2/xy×x2+2xy+y2/x2-xy 的值.

Answer 1

你好

x²+y²-10x-6y+34=0
（x-5）²+（y-3）²=0
每项都大于等于0，只有等于0时上式才成立，所以
x=5
y=3
（x-y/x+y）²÷（x²-y²）/xy×（x²+2xy+y²）/（x²-xy）
=（x-y）²/（x+y）²×xy/[（x-y）（x+y）]×（x+y）²/x（x-y）
=y/（x+y）
=3/8

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Answer 2

x2+y2-10x-6y+34=0
x²-10x+25+y²-6y+9=0
(x-5)²+(y-3)²=0
∴x=5 y=3

（x-y/x+y）2÷x2-y2/xy×x2+2xy+y2/x2-xy
=(x-y)²/(x+y)²×xy/(x+y)(x-y)×(x+y)²/x(x-y)
=y/(x+y)
=3/(5+3)
=3/8