设x,y,z>0,求证 (x^4+y^4+z^4)-4(y+z)x^3-4(z+x)y^3-4(x+y)z^3 +17[(yz)^2+(zx)^2+(xy)^2]-10xyz(x+y+z)>=0 (一)x=max(x,y,z)[x^2-3x(y+z)+4(y^2+z^2)+3yz](x-y)(x-z)+[10x^2+y^2+z^2-6yz)*(y-z)^2>=0(二)Σ(10x^ 展开
设x,y,z>0,求证 (x^4+y^4+z^4)-4(y+z)x^3-4(z+x)y^3-4(x+y)z^3 +17[(yz)^2+(zx)^2+(xy)^2]-10xyz(x+y+z)>=0 (一)x=max(x,y,z)[x^2-3x(y+z)+4(y^2+z^2)+3yz](x-y)(x-z)+[10x^2+y^2+z^2-6yz)*(y-z)^2>=0(二)Σ(10x^2+y^2+z^2-6yz)*(y-z)^2>=0(三)(x^2-2xy-2xz+3yz)^2+(y^2-2yz-2xy+3zx)^2+(z^2-2zx-2yz+3xy)^2>=0 收起
