1. The problem statement, all variables and given/known data I am a Turkish student bogged down by a very difficult question (at least for me). Here's the question: Given that xy= 1, find all solutions for X4 + y4 - z4 + 4z2 - 2 = 0. I've spent many hours on this equation. It even prevents me from sleep. I would appreciate it deeply if someone were to solve it for me, but I'll be equally grateful being directed to a book where equations of this kind are handled. Is this a trivial question? Is it simple to answer with the necessary background? 2. Relevant equations the multiplication of xy is constant and equal to 1. 3. The attempt at a solution I have tried various ways of expanding it, tried to rewrite the z part as binomial, but I think this is just beyond my skill. Thanks so much for pputting up with my desperation! Any response is appreciated very much.