Question 18
Let $a$, $b$, and $c$ be real numbers such that
$$
\begin{aligned}
a + b + c &= 100 \\
ab + bc + ca &= 20, \text{ and } \\
(a + b)(a + c) &= 24
\end{aligned}
$$
Compute all possible values of $bc$.
$$
\begin{aligned}
a + b + c &= 100 \\
ab + bc + ca &= 20, \text{ and } \\
(a + b)(a + c) &= 24
\end{aligned}
$$
Compute all possible values of $bc$.