I am trying to prove that maximum of $x+2y-3z$ (where $x,y,z$ are real numbers) exists under these two consitions:
$x^2-3xy+z^2 \le 5$
and
$4x^2-2xy + y^2 +4xz +10z^2 = 100$
I have spent some time on this question but find it hard. May I please ask for a solution or some idea and hints?
Thanks in advance!