中文摘要：

通过求二阶导数或列举反例的方法可解决《常用不等式（第四版）》末尾提出的问题3、问题13和问题62,另外,利用Lyapunov不等式及Moran不等式可给出其问题190中一个不等式的下界.

英文摘要：

In this paper we make use of second order derivative and counterexample to prove or disprove three inequalities appeared at the end of the book Applied Inequalities,4th ed.,by Kuang Jichang.A lower bound of an inequality is also provided by the use of Lyapunov inequality and Moran inequality.