Question 75
Let $a$, $b$, $c$ be positive and $abc = 1$. Prove that
$$
\frac{1 + ab^2}{c^3} + \frac{1 + bc^2}{a^3} + \frac{1 + ca^2}{b^3} \geq \frac{18}{a^3 + b^3 + c^3}.
$$
Determine when equality is attained.
$$
\frac{1 + ab^2}{c^3} + \frac{1 + bc^2}{a^3} + \frac{1 + ca^2}{b^3} \geq \frac{18}{a^3 + b^3 + c^3}.
$$
Determine when equality is attained.