(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Cubic Roots

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