Question 74
Suppose $a$, $b$, and $c$ are complex numbers satisfying
$$
\begin{aligned}
a^{2} & = b - c, \\
b^{2} & = c - a, \text{ and } \\
c^{2} & = a - b .
\end{aligned}
$$
Compute all possible values of $a + b + c$.
$$
\begin{aligned}
a^{2} & = b - c, \\
b^{2} & = c - a, \text{ and } \\
c^{2} & = a - b .
\end{aligned}
$$
Compute all possible values of $a + b + c$.