论文部分内容阅读
证明不等式是数学竞赛中的热点,因此研究不等式的证明方法也是研究数学竞赛的重点内容之一. 本文通过利用基本不等式a2≥2n-1,当且仅当a=1时取等号,以及其推广来解决数学竞赛中一类不等式的证明问题.这种方法简捷、易于操作,且具有一般性,但运用时要注意等号成立的条件.下面举例说明. 例1 设x1,x2,…,xn∈R+,求证(x12)/x2+(x22)/x3+…+(xn-12)/xn+xn2/x1≥x1+x2+…+xn.
The proof of inequality is a hotspot in mathematics competition. Therefore, the proof method of studying inequality is also one of the focuses of the study of mathematics competition. This article uses the basic inequality a2≥2n-1, if and only if a=1, and the equal sign, and its Promote to solve the problem of proof of a type of inequality in the mathematical competition. This method is simple, easy to operate, and general, but it should pay attention to the condition that the equal sign is established. Here is an example to illustrate. Example 1 Let x1, x2,..., xn∈R+, verification (x12)/x2+(x22)/x3+...+(xn-12)/xn+xn2/x1≥x1+x2+...+xn.