Question

x2+xy+y2; y2+yz+z2; x2+xz+z2 find x,y,z'

Answer 1

x2+ y2+ z2- xy- yz- xz= 0

Now, multiple by two and split them.

x2+ y2– 2xy+ y2+ z2– 2yz+ x2+ z2– 2xz= 0

Now cluster them:

(x-y)2+ (y-z)2+ (x-z)2= 0

Since squares can not be negative, each of these terms should be zero. This means,

x=y,

y=z,

x=z.

x=y=z. Simple.