x^5+y^5-x^4y-xy^4=x^4(x-y)-y^4(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)=(x^2+y^2)(x+y)(x-y)^2x,y为互不相等的正数x^2+y^2>0x+y>0x-y不等于0所以(x-y)^2>0所以(x^2+y^2)(x+y)(x-y)...