Nesbitt不等式:若a,b,c∈R+,则a/b+c+b/c+a+c/a+b≥32.该不等式可参见高中新课程人教版高中教材《不等式选将》第49页习题第7题,它也曾经作为1963年俄罗斯数学竞赛试题出现,其证明方法有多种,但基本上都是变形复杂、计算量大,对学生来讲可操作性不高.笔者最近在竞赛辅导中得到了该不等式的一个简洁证法,同时对该不等式作了进一步探究,得到几个有趣的结果,现与大家分享. Nesbitt inequality: if a, b, c ∈ R +, a / b + c + b / c + a + c / a + b ≥ 32. The inequality can be found in the high school new curriculum PEP senior high school textbook “inequality election will” Problem 49, Problem 7, which also appeared as a test for the Russian Mathematical Contest in 1963, has many ways of proving it, but it is basically complicated, computationally intensive, and not practical for students. Recently, a conciseness proof of this inequality was obtained in the competition counseling. At the same time, the inequality was further explored and several interesting results were obtained. Now we share with you.