关于无理不等式的证明,近来有许多文章(如文[1]、[2]、[3]等)都介绍了一种的证明方法:等号成立条件法.在此应用“方差”对其中一类无理不等式给出初中学生也能理解的简洁证法.方差是初中代数《统计初步》中的一个重要概念.S~2=(1/n)[(x_1- )~2+(x_2- )~2+…+(x_n- )~2]其中 =(1/n)(x_1+x_2+…+x_n),S~2表示方差,显见 With regard to the proof of irrational inequalities, many recent articles (eg, articles [1], [2], [3], etc.) have introduced a method of proof: the equal sign is established with the conditional method. Here the “variance” is applied to one of them. The class-irrational inequality gives a concise proof that junior middle school students can also understand. Variance is an important concept in junior high school algebra “Statistical preliminary”. S~2=(1/n)[(x_1- )~2+(x_2-)~ 2+...+(x_n-)~2] where =(1/n)(x_1+x_2+...+x_n) and S~2 represents the variance, obviously