若两个正实数x,y满足x^2+2xy-3y^2=0,求x^2+xy+y^2/x^2-xy+y^2
问题描述：
若两个正实数x,y满足x^2+2xy-3y^2=0,求x^2+xy+y^2/x^2-xy+y^2
答
x^2+2xy-3y^2=0
x^2+2xy+y^2-4y^2=0
(x+y)^2=4y^2
x+y=2y或x+y=-2y
x=y或x=-3y
因为两个正实数
所以x=y
x^2+xy+y^2/x^2-xy+y^2
=（x^2+x^2+x^2)/(x^2-x^2+x^2)
=3x^2/(x^2)
=3