多元变量最值问题在各类模拟试题中出现频率高,学生往往感到入手难、处理难,本文通过两道模拟试题的分析谈谈一类多元变量最值问题的常见解法.例1(2015届高三苏锡常镇三模第14题)已知a,b∈R,a≠0,曲线y=a+2/x,y=ax+2b+1在区间[3,4]上至少有一个公共点,则a~2+b~2的最小值为.解法一(减元法) The multivariate variable maximum value problem appears frequently in all kinds of simulated test questions, and the students often find it difficult to start with and deal with difficulties. In this paper, we discuss two common problems of multivariate variables through the analysis of two simulated test questions. So, we know that a, b∈R, a ≠ 0, the curve y = a + 2 / x, y = ax + 2b + 1 There is at least one common point in the interval [3,4] , The minimum value of a ~ 2 + b ~ 2 is 1. Solution 1 (Subtraction method)