Question 110
Given a system of equations on $\mathbb{R}$
$$
\begin{cases}
x - ay = yz \\
y - az = zx \\
z - ax = xy
\end{cases}
$$
a) Solve that system when $a = 0$.
b) Prove that the system has 5 different roots when $a \gt 1$.
$$
\begin{cases}
x - ay = yz \\
y - az = zx \\
z - ax = xy
\end{cases}
$$
a) Solve that system when $a = 0$.
b) Prove that the system has 5 different roots when $a \gt 1$.