设A=x^2+y^2+z^2-xy-yz-zx;2A=2x^2+2y^2+2z^2-2xy-2yz-2zx;2A=(x-y)^2+(y-z)^2+(z-x)^2 =m^2+3^2+(m-3)^2 =m^2+9+m^2-6m+9 =2m^2-6m+18所以A=m^2-6m+9+3m=（m-3)^2+3m（m-3）最小值为0；所以最小值为3m
