Question 170
Prove that if $a$, $b$, $c$ are positive real numbers such that $abc = 1$, then
$$
(1 + a^3)(1 + b^3)(1 + c^3) \ge 2 \left(1 + \frac{b}{a} + \frac{c}{b} + \frac{a}{c}\right).
$$
$$
(1 + a^3)(1 + b^3)(1 + c^3) \ge 2 \left(1 + \frac{b}{a} + \frac{c}{b} + \frac{a}{c}\right).
$$