Question

设x,y,z>0,求证：（x+y+z)^5-(x^5+y^5+z^5)>=10(x+y)(y+z)(z+x)(xy+yz

Answer 1

令f(x,y,z)=(x+y+z)^5-(x^5+y^5+z^5).易知f(x,y,z)是对称式.当x+y=0是,f(x,y,z)=0,所以（x+y）| f(x,y,z),从而（y+z）|f(x,y,z),(z+x)|f(x,y,z).所以（x+y)(y+z)(z+x)|f,注意到f是关于x,y,z的五次齐次式,故可设f（x,...