• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Multivariate quartic function help

  • Thread starter rattam
  • Start date
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.
Last edited:
I would say the solution is some kind of a line on the xy=1 plane in 3D. Your solution would be a closed form of an equation. So I don't know if saying that
{(x,1/x,z) satisfying the equation x^4+1/x^4-z^4-4z^2-2=0 }
is the solution set is enough.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving