Question 5
Consider the real system with parameter $a$:
$$\begin{cases}x-ay=yz,\\ y-az=zx,\\ z-ax=xy.\end{cases}$$
a) Solve the system when $a=0$.
b) Prove that the system has five distinct solutions for every real $a\gt 1$.
$$\begin{cases}x-ay=yz,\\ y-az=zx,\\ z-ax=xy.\end{cases}$$
a) Solve the system when $a=0$.
b) Prove that the system has five distinct solutions for every real $a\gt 1$.