设xy为正数,且满足x2-2xy-y2=2xy 求x+y分之x-y的值

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设xy为正数,且满足x2-2xy-y2=2xy 求x+y分之x-y的值
sorry.打错了。
设xy为正数，且满足x2-2xy-y2=0 求x+y分之x-y的值

x2-2xy-y2=2xy
x²-y²=4xy
两边同除以y²得：
(x/y)²-4(x/y)-1=0
[(x/y)-2]²=5
x/y=2+√5；x/y=2-√5(＜0；舍去)
x+y分之x-y
分子分母同除以y得：
原式=(x/y-1)/(x/y+1)
=(√5+1)/(√5+3)
=(√5+1)(3-√5)/4
=(3-5+2√5)/4
=(√5-1)/2

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