The discussion focuses on solving the nonlinear equation system defined by the relationships \(\frac{y+z}{a} = \frac{x+z}{b} = \frac{x+y}{c} = xyz\), where \(a\), \(b\), and \(c\) are non-zero constants. Participants explored various approaches to derive solutions for \(x\), \(y\), and \(z\), ultimately identifying the trivial solution (0,0,0) and suggesting a method to rewrite the equations for further analysis. The recommended approach involves substituting variables \(p\), \(q\), and \(r\) to simplify the equations and derive non-zero solutions.
PREREQUISITESStudents, mathematicians, and anyone interested in solving complex nonlinear equations, particularly those studying algebra or advanced mathematics.
dirk_mec1 said:Homework Statement
Solve x,y and z from <br /> \frac{y+z}{a}= \frac{x+z}{b}=\frac{x+y}{c} = xyz<br />
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).
dirk_mec1 said:Homework Statement
Solve x,y and z from <br /> \frac{y+z}{a}= \frac{x+z}{b}=\frac{x+y}{c} = xyz<br />
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).