Question 50
Let $a$, $b$, $c$ be fixed real numbers, where $0 \le a, b, c \le 4$. Prove that the system of equations
$$
\begin{cases}
p^2 - a q = -3 \\
q^2 - b r = -4 \\
r^2 - c p = -5
\end{cases}
$$
has no real solutions ($p$, $q$, $r$).
$$
\begin{cases}
p^2 - a q = -3 \\
q^2 - b r = -4 \\
r^2 - c p = -5
\end{cases}
$$
has no real solutions ($p$, $q$, $r$).