不等式证明是数学竞赛的热点、难点,也是初等数学研究的热点之一.本文给出一个平凡不等式(即下面的不等式1),并举例说明它在各类数学竞赛中的应用.若x>0,y>0,则1/x+1/y≥4/x+y(1)这是关于x,y的二元分式不等式,有很多证明方法,如作差法、分析法、柯西不等式法等.深掘此不等式,内涵丰富,韵味十足,有极其丰富的应用空间.下面我们应用不等式(1)来证明若干数学竞赛试题.例1(2011年全国高中数学联赛贵州省预 Inequality proves to be a hot and difficult problem in mathematics competition. It is also one of the focuses of elementary mathematics research. This paper gives a trivial inequality (ie inequality 1 below) and gives an example of its application in various types of mathematical competition. If x>0 ,y>0, then 1/x+1/y≥4/x+y(1) This is a binary fractional inequality about x,y. There are many proof methods, such as difference method, analysis method, and Cauchy. Inequality method, etc. Deep digging this inequality, connotation rich, full of flavor, there is an extremely rich application of space. Here we apply inequality (1) to prove a number of math contest questions. Example 1 (2011 National High School Mathematics League Guizhou Province pre