Question 108
Suppose $a$, $b$, and $c$ are real numbers such that
$$
\begin{aligned}
a^{2} - b c &= 14 \\
b^{2} - c a &= 14, \text{ and } \\
c^{2} - a b &= -3
\end{aligned}
$$
Compute $|a+b+c|$.
$$
\begin{aligned}
a^{2} - b c &= 14 \\
b^{2} - c a &= 14, \text{ and } \\
c^{2} - a b &= -3
\end{aligned}
$$
Compute $|a+b+c|$.