1. The problem statement, all variables and given/known data Let F(x,y) be a twice differentiable function such that 4 * Fx2 + Fy2 = 0. Set x = u2 - v2 and y = u*v. Show that Fu2 + Fv2 = 0 3. The attempt at a solution Fu = Fx*2u + Fy*v Fv = Fx*-2v + Fy*u Fu2 = 4v2Fx2-4FxFy*u*v+Fy2u2 Fv2 = 4u2Fx2+4FxFy*u*v+Fy2v2 Adding these two together gives 4Fx2*(u2v2) + 4Fy2*(u2v2), Which from our first equation, can clearly equal zero if we factor out the (u2v2) and divide. Then, we see that, indeed, Fu2 + Fv2 = 0. Sound about right?