2008 IMO Shortlist A5

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

设 $a, b, c, d$ 为正实数，使得 $$a b c d=1 \quad \text { 和 } \quad a+b+c+d>\frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{a}$$ 证明 $$a+b+c+d<\frac{b}{a}+\frac{c}{b}+\frac{d}{c}+\frac{a}{d}$$