I ran into a case where Mathematica Solve yields different solutions depending on whether I solve it analytically (and then plug in some numbers) or numerically. I'm solving an algebraic equation, with some square roots. Mathematica does NOT complain about branch cut or anything else when solving the problem analytically. Based on physical reasoning that created the equation in the 1st place the purely numerical solution is the correct one. I attached a 3-line pdf version of the notebook that demonstrates this issue. Thank you for any suggestions!