正数x y 满足（x²-y²)/x*y=2 求x-y/x+y的值
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x²-y²=2xy,∴(x-y)(x+y)=2xy,∴(x-y)/(x+y)=(x-y)²/(x²-y²)=(x²-2xy+y²)/2xy=[x²+y²-(x²-y²)]/2xy=2y²/2xy=y/x又由x²-y²=2xy,得x/y-y/x=2,即（y/x)²+2(y/x)-1=0∴y/x=-1+√2或y/x=-1-√2(舍去，因为X，Y都是正数。即（x-y)/(x+y)=√2-1
x²-y²=2xy,∴(x-y)(x+y)=2xy,∴(x-y)/(x+y)=(x-y)²/(x²-y²)=(x²-2xy+y²)/2xy=[x²+y²-(x²-y²)]/2xy=2y²/2xy=y/x又由x²-y²=2xy,得x/y-y/x=2,即（y/x)²+2(y/x)-1=0∴y/x=-1+√2或y/x=-1-√2(舍去，因为X，Y都是正数。即（x-y)/(x+y)=√2-1
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