Question 124
Let $a$, $b$ and $c$ be three strictly positive numbers such that $a + b + c + abc = 4$. Show that
$$
\left(1 + \frac{a}{b} + ca\right)\left(1 + \frac{b}{c} + ab\right)\left(1 + \frac{c}{a} + bc\right) \geqslant 27
$$
$$
\left(1 + \frac{a}{b} + ca\right)\left(1 + \frac{b}{c} + ab\right)\left(1 + \frac{c}{a} + bc\right) \geqslant 27
$$