浅探算术-几何均值不等式在不等式证明中的应用

On the Application of Arithmetic and Geometric Mean Inequality in the Proof of Inequality

均值不等式是数学中几个经典不等式之一,在生产和生活中具有重要作用,是证明不等式及求解各类最值问题的一个重要依据和方法。其中算术-几何均值不等式应用最为广泛,具有变通灵活性和条件约束性等特点,在不等式证明方面具有不可忽视的作用。本文分别从内容的突破和形式的构造两个方面,探索算术-几何均值不等式在不等式证明中的应用。

The mean value inequality is one of several classical inequality in mathematics,It plays an important role in production and life,It proves an important basis and method for inequality and solving the eigenvalue problem. The arithmetic and geometric mean inequality is most widely used,with varying characteristics and constraints of psychic activity,The proof of inequality has a role and can not be ignored.Two aspects are constructed in this paper separately from the content and form of the breakthrough,exploring the application of arithmetic and geometric mean inequality in the proof of inequality.