Question 9
Let $a$, $b$, $c$, $d$ be positive real numbers such that
$$
a b c d = 1 \quad \text{ and } \quad a + b + c + d \gt \frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a}
$$
Prove that
$$
a + b + c + d \lt \frac{b}{a} + \frac{c}{b} + \frac{d}{c} + \frac{a}{d}
$$
$$
a b c d = 1 \quad \text{ and } \quad a + b + c + d \gt \frac{a}{b} + \frac{b}{c} + \frac{c}{d} + \frac{d}{a}
$$
Prove that
$$
a + b + c + d \lt \frac{b}{a} + \frac{c}{b} + \frac{d}{c} + \frac{a}{d}
$$