4x^3-4x^2y-xy^2+y^3=0

4x^3-4x^2y-xy^2+y^3=0
4x^3-4x^2y+xy^2-2xy^2+y^3=0
x(4x^2-4xy+y^2)-2xy^2+y^3=0
x(2x-y)^2-y^2(2x-y)=0
(2x-y)(2x^2-xy-y^2)=0
(2x-y)(2x^2-2xy+xy-y^2)=0
(2x-y)[2x(x-y)+y(x-y)]=0
(2x-y)(2x+y)(x-y)=0
所以2x-y=0或2x+y=0或x-y=0
若2x-y=0
则y=2x
(x^2+y^2)/xy
=(x^2+4x^2)/(2x*x)
=5/2
若2x+y=0
则y=-2x
(x^2+y^2)/xy
=(x^2+4x^2)/(-2x*x)
=-5/2
若x-y=0
则y=x
(x^2+y^2)/xy
=(x^2+x^2)/(x*x)
=2