比较大小：x^5+y^5和x^4+xy^4
问题描述：
比较大小：x^5+y^5和x^4+xy^4
答
x^5+y^5-(x^4y+xy^4)=x^4-x^4y+y^5-xy^4=x^4(x-y)+y^4(y-x)=(x-y)(x^4-y^4)=(x-y)(x^2+y^2)(x^2-y^2)=(x-y)(x^2+y^2)(x+y)(x-y)=(x-y)^2(x+y)(x^2+y^2)＞0所以x^5+y^5＞x^4y+xy^4.