1. The problem statement, all variables and given/known data The equation: x^3 + ax + b = 0 has 3 roots, u, p and q. Give the general solution for for an equation with roots (u/p)+(p/u), (p/q)+(q/p) and (u/q)+(q/u) 2. Relevant equations u + p + q = 0 upq = -b up + uq + pq = a If you can solve it you probably already knew those. 3. The attempt at a solution Well I've just done lots of fiddling with algebra and got a pretty nasty looking solution, and I'm not even sure if it's right. What I was trying to do was express one of the new roots in terms of a, b and u, and then plug back in to the original equation for the new equation. I've got a pretty rough looking solution but I wanted to see if anyone could find a elegant way of solving this or if it is just lots of scruffy algebra. Thanks.