I am trying to find the stationary points of the potential $U(x,y)=x^2+y^2$ with constraint $x^2-2y^2=1$
So I set the Augmented potential $U^*=x^2+y^2+m(x^2-2y^2)$ where $m$ is the Lagrange multiplier
Then we need ${\partial U^*\over \partial x}={\partial U^*\over \partial y}={\partial U^*\over \partial z}=0$
In other words $(1+m)x=(1-2m)y=0$
together with the constraint equation $x^2-2y^2=1$ should give $m$ but all I get is $x^2+y^2+m=0$ but $m$ is supposed to be obtainable as a constant.
Could somebody tell me what has gone wrong? Thank you.