Question

If x,y,z are real numbers such that #x^2+y^2+2z^2=4x-2z+2yz-5# then #x-y-z=?#

Answer 1

what math is this?

Answer 2

\(x^2+y^2+2z^2=4x-2z+2yz-5\)
\(x^2-4x+4+y^2+2z^2=-2z+2yz-1\)
\((x+2)^2+y^2-2yz+z^2+z^2=-2z-1\)
\((x+2)^2+(y-z)^2+z^2=-2z-1\)
\((x+2)^2+(y-z)^2+z^2+2z+1=0\)
\((x+2)^2+(y-z)^2+(z+1)^2=0\)
\(x=-2\)
\(y-z=0\)
\(z=-1\)

\(x=-2, y=-1, z=-1\)
\(x-y-z=-2+1+1=0\)