Puzzle of the Week #166 - Cubic Conundrum


(x + 1/x) = 7

what is

(x^3 + 1/x^3) ?

This being a puzzle rather than just a maths problem, there is of course a way to solve it without having to go through the messy business of working out what x is equal to. You might even want to let (x + 1/x) = A and then express (x^3 + 1/x^3) purely in terms of A.