已知x,y,z>=0,求证 (x^3+y^3+z^3)^2-2(x^4+y^4+z^4)*(yz+zx+xy)+4xyz(y+z)(z+x)(x+y)-7(xyz)^2>0配方得 (x^3+y^3+z^3)^2-2(x^4+y^4+z^4)(yz+zx+xy)+4xyz(y+z)(z+x)(x+y)-7(xyz)^2=[(2x+y+z)*(2y+z+x)*(2z+x+y)-9*(y+z 展开
已知x,y,z>=0,求证 (x^3+y^3+z^3)^2-2(x^4+y^4+z^4)*(yz+zx+xy)+4xyz(y+z)(z+x)(x+y)-7(xyz)^2>0配方得 (x^3+y^3+z^3)^2-2(x^4+y^4+z^4)(yz+zx+xy)+4xyz(y+z)(z+x)(x+y)-7(xyz)^2=[(2x+y+z)*(2y+z+x)*(2z+x+y)-9*(y+z)*(z+x)*(x+y)]^2/4 +(y-z)^2*(z-x)^2*(x-y)^2>0 收起
