Question 8
Suppose $a$, $b$, $c$ are real numbers such that $a + b + c = 0$ and $a^2 + b^2 + c^2 = 1$. Prove that
$$
a^2 b^2 c^2 \leq \frac{1}{54}
$$
and determine the cases of equality.
$$
a^2 b^2 c^2 \leq \frac{1}{54}
$$
and determine the cases of equality.