本文从一道河南省选拔优秀专科生进入本科学校考试真题——等式证明题出发,通过构造辅助函数的方法,利用朗格拉日中值定理可以证明等式和不等式. In this paper, starting from a Henan Province, the selection of outstanding junior college students into the undergraduate exam Zhenti - equation proof questions starting by constructing auxiliary functions, the use of Languedoc’s median theorem can prove equations and inequalities.