试比较x^3+y^3与x^2y+xy^2的大小
问题描述：
试比较x^3+y^3与x^2y+xy^2的大小
答
做差:
(x^3+y^3)-(x^2y+xy^2)
=(x^3-x^2y)+(y^3-xy^2)
=x^2(x-y)+y^2(y-x)
=(x+y)(x-y)^2
若x=y或x=-y
则x^3+y^3=x^2y+xy^2
若x>-y且x≠y
则x^3+y^3>x^2y+xy^2
若x