高中数学问题-1

对于任意实数,求证 f(x,y,z)=6x^2+27y^2+61z^2-62yz-8zx-12xy>=0配方得:f(x,y,z)=(2x-y-3z)^2+(x5y+6z)^2+(x+y-4z)^2f(x,y,z)=2(3x-3y-2z)^2/3+7(3y-5z)^2/3当x:y:z=7:5:3取等号.