已知1/x-1/y=1/(x+y),则x^2/y^2+y^2/x^2的值.
问题描述：
已知1/x-1/y=1/(x+y),则x^2/y^2+y^2/x^2的值.
答
1/x-1/y=1/(x+y)
(y-x)/xy=1/(x+y)
(y-x)(y+x)=xy
y²-x²=xy
(y²-x²)²=(xy)²
(y^4)-2(xy)²+(x^4)=(xy)²
(x^4)+(y^4)=3(xy)²
((x^4)+(y^4))/((xy)²)=3
x^2/y^2+y^2/x^2=((x^4)+(y^4))/((xy)²)=3