原式=1/2[(x-y)2+(x-z)2+(y-z)2]又x-y=m,y-z=n,所以,x-z=m+n, 代入原式。即得m2+n2+mn
x^2+y^2+z^2-xy-yz-zx=x(x-y)+y(y-z)+z(z-x)=mx+ny-z(m+n)=m(x-z)+n(y-z)=m(m+n)+n*n
x-z=x-y+y-z=m+n