不等式的证明存在着寻找入口难 ,条件运用难 ,确定变形方向难等问题 .本文从一道IMO试题证明入手 ,从多方向考虑 ,探求其一般的思路 ,使学生能举一反三 .例　 (第 2 0届IMO试题 )设x1 ,x2 ,… ,xn是两两互不相同的正整数 ,求证对任何正整数n ,有x1 1 2 + x22 2 +… + xnn2 ≥ 1 The inequality proves that it is difficult to find the entrance, the conditions are difficult to apply, and the direction of the deformation is difficult to determine. This article starts with an IMO test and considers it from multiple directions to explore its general ideas, so that students can give an inverse picture. (The 20th session IMO questions) Let x1,x2,...,xn be positive integers that are different from each other. Verify that for any positive integer n, there are x1 1 2 + x22 2 +... + xnn2 ≥ 1