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: Non linear equation

  1. Oct 8, 2013 #1
    1. The problem statement, all variables and given/known data
    Solve x,y and z from [tex]
    \frac{y+z}{a}= \frac{x+z}{b}=\frac{x+y}{c} = xyz
    [/tex]

    wit a,b,c not equal to zero.

    2. Relevant equations



    3. The attempt at a solution
    I have no idea how to start. I've tried several things but it seems like I'm missing something. I did find the trivial solution (0,0,0).
     
  2. jcsd
  3. Oct 8, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You say you tried several things. What were they? You need to show your work.
     
  4. Oct 8, 2013 #3
    Rewrite the equation as
    $$\frac{1}{a}\left(\frac{1}{xz}+\frac{1}{xy}\right)=\frac{1}{b} \left( \frac{1}{yz}+\frac{1}{xy}\right)=\frac{1}{c}\left(\frac{1}{yz}+\frac{1}{xz}\right)=1$$
    Substitute ##1/(xy)=p, 1/(yz)=q## and ##1/(xz)=r##. Form three equations to find p, q and r. This gives the possible non-zero solutions.
     
  5. Oct 8, 2013 #4
    Understood, thanks.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted