Question

已知x=2m-n-k,y=2n-k-m,z=2k-m-n,试问代数式(n-k)x+(k-m)y+(m-n)z的值是否会随

Answer 1

不变,原式=0

原式=（n-k)(2m-n-k)+(k-m)(2n-k-m)+(m-n)(2k-m-n)

=2mn-2mk-(n^2-k^2)+2nk-2mn-(k^2-m^2)+2mk-2nk-(m^2-n^2)

=k^2-n^2-k^2+m^2-m^2+n^2

=0