Question

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

Answer 1

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