Question

试比较x^3+y^3与x^2y+xy^2的大小

Answer 1

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