文献[1]对北师大版高中教材《数学》(选修2-2)中的一道习题予以研究,给出了多种证明方法,并将结论进行推广,得到两个新命题。遗憾的是,文中的第3种证法出现了两处错误。鉴于这两种错误在学生中也具有一定的普遍性,本文对其予以订正,并给出原不等式的一个再推广。1题目及证法再现 Literature [1] studied a series of exercises in “Mathematics” (elective 2-2) of the teaching materials of Beijing Normal University High School, gave a variety of proof methods, and popularized the conclusions and got two new propositions. Unfortunately, there are two mistakes in the third proof in the article. In view of the fact that these two kinds of errors also have a certain universality among students, this paper will correct them and give a further generalization of the original inequality. 1 title and card law reproduction