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所谓复合最值就是在一群最大(小)值中求最值。其思考方法有以下几种。一、算术平均值法若M,m分别是变数a_1,a_2,…a_n中的最大者与最小者,则对a_1,a_2,…,a_n中任意几个数的算术平均值A均有 M≥A≥m。这虽是一个简单的事实,却应用广泛且易被人忽视。例1 求单位圆内接四边形的最短边的最大值。(82年上海中学数学竞赛试题) 解记圆内接四边形ABCD各边所对劣弧度数分别为AB,BC,CD,DA,则最短边所对劣弧度数小于等于故单位圆最短边的最大值为2sinπ/4=2~(1/2)。此时四
The so-called composite best value is to find the best value among a group of the largest (small) values. There are several ways to think about it. First, the arithmetic average method If M, m are the largest and the smallest of the variables a_1, a_2, ... a_n, then the arithmetic mean A of any number of a_1, a_2, ..., a_n has M ≥ A≥m. Although this is a simple fact, it is widely used and easily overlooked. Example 1 Find the maximum value of the shortest edge of the inscribed quad of the unit circle. (82th Shanghai High School Mathematics Contest Question) The number of bad arcs on each side of the inscribed quadrilateral ABCD is AB, BC, CD, DA. The shortest side arc is less than or equal to the shortest side of the unit circle. The value is 2sinπ/4=2~(1/2). At this time four