1995 IMO 第 6 题

A6 (JAP) Let $n$ be an integer, $n \geq 3$. Let $x_{1}, x_{2}, \ldots, x_{n}$ be real numbers such that $x_{i}<x_{i+1}$ for $1 \leq i \leq n-1$. Prove that $$\frac{n(n-1)}{2} \sum_{i<j} x_{i} x_{j}>\left(\sum_{i=1}^{n-1}(n-i) x_{i}\right)\left(\sum_{j=2}^{n}(j-1) x_{j}\right) .$$

A6 (JAP) 令 $n$ 为整数，$n \geq 3$。令 $x_{1}, x_{2}, \ldots, x_{n}$ 为实数，使得 $x_{i}<x_{i+1}$ 为 $1 \leq i \leq n-1$。证明 $$\frac{n(n-1)}{2} \sum_{i<j} x_{i} x_{j}>\left(\sum_{i=1}^{n-1}(n-i) x_{i}\right)\left(\sum_{j=2}^{n}(j-1) x_{j}\right) 。$$