1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Multivariate quartic function help

  1. Dec 7, 2009 #1
    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: Dec 7, 2009
  2. jcsd
  3. Jan 3, 2010 #2
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook