2014年“北约”自主招生考试压轴题(第10题)为:已知x1,x2,…,xn∈R+,满足x1x2…xn=1,求证:(2~(1/2)+x1)(2~(1/2)+x2)…(2~(1/2)+xn)≥(2~(1/2)+1)n.作为“北约”自主招生考试的压轴题,这道不等式证明题条件简洁、形式对称、结构优美,难度与全国联赛试题相当,具有较好的区分度和选拔功能.一、试题的多种证法这道试题的证明方法较多,本文介绍其中比较 In 2014, the “Nato” self-enrollment exam finale (Question 10) is: Known x1, x2, ..., xn∈R +, satisfy x1x2 ... xn = 1, (2 ~ (1/2) + x2) ... (2 ~ (1/2) + xn) ≥ (2 ~ (1/2) +1) n.As the norm of the “NATO” independent admission examination , This road inequalities proves that the conditions are simple, symmetrical in form, beautiful in structure, and the difficulty is comparable to the national league test, with a good distinction and selection function. Introduction to which comparison