Question 66
Let $a$, $b$ and $c$ be positive real numbers such that $a b c = \frac{1}{8}$. Prove the inequality
$$
a^{2} + b^{2} + c^{2} + a^{2} b^{2} + b^{2} c^{2} + c^{2} a^{2} \geq \frac{15}{16}
$$
When does equality hold?
$$
a^{2} + b^{2} + c^{2} + a^{2} b^{2} + b^{2} c^{2} + c^{2} a^{2} \geq \frac{15}{16}
$$
When does equality hold?