设x-3y+2z=0,试证明x^2-9y^2+4z^2+4xz+2100为定值

问题描述:

设x-3y+2z=0,试证明x^2-9y^2+4z^2+4xz+2100为定值

x^2-9y^2+4z^2+4xz+2100
=x^2+4z^2+4xz-9y^2+2100
=(x+2z-3y)(x+2z+3y)+2100
=2100