已知xy≠0且
x^3+2x^2y-xy^2-2y^3=0
(x^3-y^3)+2x^2y-xy^2-y^3=0
(x-y)(x^2+xy+y^2)+y(x^2-y^2)+xy(x-y)=0
(x-y)(x^2+2xy+y^2)+y(x+y)(x-y)=0
(x+y)(x+2y)(x-y)=0
当x=-y时
(x^2+2y^2)/xy=3y^2=-y^2=-3
当x=-2y时
(x^2+2y^2)/xy=5y^2/-2y^2=-5/2
当x=y时
(x^2+2y^2)/xy=3x^2/x^2=3