比较大小:x^5+y^5和x^4+xy^4

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比较大小:x^5+y^5和x^4+xy^4比较大小:x^5+y^5和x^4+xy^4比较大小:x^5+y^5和x^4+xy^4x^5+y^5-(x^4y+xy^4)=x^4-x^4y+y^5-xy^4

比较大小:x^5+y^5和x^4+xy^4
比较大小:x^5+y^5和x^4+xy^4

比较大小:x^5+y^5和x^4+xy^4
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.