不等式证明问题是高中数学的难点之一 ,本文展示一道题的多种证法 ,旨在说明对不等式的证明之应尽可能寻求多种思路 ,以达到培养自己的发散思维能力的目的 .例　已知a ,b ,x ,y均为正数 ,且 ax + by =1.求证 :x + y≥ (a +b) 2 .分析 1:巧添常数 1,应用基本不等式证明 .证法 1 The inequality proves that the problem is one of the difficulties of high school mathematics. This paper presents a variety of proofs of a problem, aiming to prove that the proof of inequality should seek as many ideas as possible in order to achieve the purpose of training its own divergent thinking ability. Know that a, b, x, y are all positive, and ax + by =1. Proof: x + y≥ (a + b) 2. Analysis 1: Coincidentally add a constant 1, use basic inequality proof. Proof method 1