Question 105
Let $a$, $b$, $c$ be real numbers such that the system of equations
$$
\begin{cases}
ax + by = 1 \\
x + cy = a \\
cx + y = b
\end{cases}
$$
has a real solution $(x, y)$.
Prove that $a^2 + b^2 + c^2 = 2abc + 1$.
$$
\begin{cases}
ax + by = 1 \\
x + cy = a \\
cx + y = b
\end{cases}
$$
has a real solution $(x, y)$.
Prove that $a^2 + b^2 + c^2 = 2abc + 1$.