1995 IMO 第 3 题

A3 (UKR) Let $n$ be an integer, $n \geq 3$. Let $a_{1}, a_{2}, \ldots, a_{n}$ be real numbers such that $2 \leq a_{i} \leq 3$ for $i=1,2, \ldots, n$. If $s=a_{1}+a_{2}+\cdots+a_{n}$, prove that $$\frac{a_{1}^{2}+a_{2}^{2}-a_{3}^{2}}{a_{1}+a_{2}-a_{3}}+\frac{a_{2}^{2}+a_{3}^{2}-a_{4}^{2}}{a_{2}+a_{3}-a_{4}}+\cdots+\frac{a_{n}^{2}+a_{1}^{2}-a_{2}^{2}}{a_{n}+a_{1}-a_{2}} \leq 2 s-2 n$$

A3 (UKR) 令 $n$ 为整数，$n \geq 3$。令 $a_{1}, a_{2}, \ldots, a_{n}$ 为实数，使得 $2 \leq a_{i} \leq 3$ 对于 $i=1,2, \ldots, n$。如果$s=a_{1}+a_{2}+\cdots+a_{n}$，证明$$\frac{a_{1}^{2}+a_{2}^{2}-a_{3}^{2}}{a_{1}+a_{2}-a_{3}}+\frac{a_{2}^{2}+a_{3}^{2}-a_{4} ^{2}}{a_{2}+a_{3}-a_{4}}+\cdots+\frac{a_{n}^{2}+a_{1}^{2}-a_{2}^{2}}{a_{n}+a_{1}-a_{2}} \leq 2 s-2 n$$