x^4+y^4-x^3y-xy^3=x^3(x-y)+y^3(y-x)=(x-y)(x^3-y^3)=(x-y)^2*(x^2+xy+y^2)
因为
x^2+y^2>=2xy>xy
(x-y)^2>=0
所以
x^4+y^4>=x^3y+y^3x