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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

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    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.
     
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