- 求证不等式设x,y,z为正实数,求证严格不等式(x^3+y^3+
- 设x,y,z为正实数,求证严格不等式
(x^3+y^3+z^3)^2-2(x^4+y^4+z^4)(yz+zx+xy)+4xyzΣx^2*(y+z)+(xyz)^2>0
- 设x,y,z为正实数,求证严格不等式
(x^3+y^3+z^3)^2-2(x^4+y^4+z^4)(yz+zx+xy)+4xyzΣx^2*(y+z)+(xyz)^2>0
配方得
(x^3+y^3+z^3)^2-2(x^4+y^4+z^4)(yz+zx+xy)+4xyzΣx^2*(y+z)+(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