1. The problem statement, all variables and given/known data Find all critical points of u(x,y)=(x-y)(x^2+y^2-1) 2. Relevant equations - 3. The attempt at a solution Partial differentials: ux=3x^2+y^2-1-2xy=0 uy=-x^2-3y^2+2xy+1=0 I know the critical points are the solutions to the above two equations. But how do I solve these equations? Or am I going about it the wrong way?