x-y=1+m y-z=1-m x^2+y^2+z^2-xy-xz-yz=?

x-y=1+m
y-z=1-m
相加
x-z=2

x^2+y^2+z^2-xy-yz-xz
=(2x^2+2y^2+2z^2-2xy-2yz-2xz)/2
=[(x^2-2xy+y^2)+(y^2-2yz+z^2)+(z^2-2xz+x^2)]/2
=[(x-y)^2+(y-z)^2+(z-x)^2]/2
=(1+2m+m^2+1-2m+m^2+4)/2
=3+m^2

x-z=(x-y)+(y-z)=2
x^2+y^2+z^2-xy-xz-yz
=[(x-y)^2+(y-z)^2+(x-z)^2]/2
=[(1+m)2+(1-m)^2+4]/2
=(2m^2+2+4]/2
=m^2+3

x-y=1+m
y-z=1-m

两个式子相加 x-z = 2

x^2+y^2+z^2-xy-xz-yz
=(2x^2+2y^2+2z^2-2xy-2xz-2yz)/2
=[(x-y)^2 + (x-z)^2 + (y-z)^2] /2
=[(1+m)^2 + 2^2 + (1-m)^2]/2
=(1+2m+m^2+4+1-2m+m^2)/2
=3+m^2