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

Non linear equation

  • Thread starter dirk_mec1
  • Start date
  • #1
761
13

Homework Statement


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.

Homework Equations





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).
 

Answers and Replies

  • #2
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728

Homework Statement


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.

Homework Equations





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).
You say you tried several things. What were they? You need to show your work.
 
  • #3
3,812
92

Homework Statement


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.

Homework Equations





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).
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.
 
  • #4
761
13
Understood, thanks.
 

Related Threads on Non linear equation

Replies
4
Views
17K
Replies
2
Views
549
  • Last Post
Replies
3
Views
2K
Replies
4
Views
13K
Top