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+3y)(x-y) = 0
x=-3y, or x=y
x>0, y>0, x= y
x^2+xy+y^2/x^2-xy+y^2
= 3
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