x^5+y^5-x^4y-xy^4=x^4(x-y)-y^4(x-y)=(x-y)(x^4-y^2)=(x-y)(x^2+y^2)(x+y)(x-y)=(x-y)^2(x^2+y^2)(x+y)x>0,y>0,x≠y所以(x-y)^2>0,(x^2+y^2)>0,(x+y)>0所以x^5+y^5-x^4y-xy^4〉0所以x^5+y^5>x^4y+xy^4