Question 5
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
$$
a+b+c+d\lt \frac{b}{a}+\frac{c}{b}+\frac{d}{c}+\frac{a}{d}
$$