近年来,构造法解题已越来越为人们所重视和运用。因为它可以启迪人的思维,激发人的想象力的创造性,对于培养思维品质,提高解题能力都有重要的作用。本文以求一个多元函数的条件最值为例,说明构造法的奇妙作用。例已知x,y,z∈R~+,且 x+y+z=1 ① x~2+y~2+z~2=1/2 ②求υ=xyz的最大值。求多元函数最值的一个基本的方法是消元,尽可能转化为一元函数来求解。不难求得该函数的定义域为x,y,z∈(0,2/3]。且x,y,z不能同时超过1/2,鉴于x,y,z的对称性,我们只需要求函数υ当其中任意一个 In recent years, the construction method has become more and more important to people. Because it can enlighten people’s thinking and stimulate the creativity of people’s imagination, it plays an important role in cultivating the quality of thinking and improving the ability to solve problems. This paper takes the conditional value of a multivariate function as an example to illustrate the wonderful effect of the construction method. For example, x,y,z∈R~+ are known, and x+y+z=1 1x~2+y~2+z~2=1/2 2 Find the maximum value of υ=xyz. One of the basic ways to find the best value of a multivariate function is to eliminate it and convert it to a one-dimensional function as much as possible. It is not difficult to find the definition of the function for the x, y, z ∈ (0, 2 / 3). And x, y, z can not exceed 1/2 at the same time, given the symmetry of x, y, z, we only need Find functions as any one of them