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每年数学高考或者竞赛中多会出现多变量的最值问题,这类问题内涵丰富、知识面广、综合性强、解法灵活多变,是考查学生运用基础知识、数学思想方法和检验学生思维灵活性的极好问题.这类问题由于变量比较多,学生往往难以找到解题思路而束手无策,或者能做但很耗时.下面举例分析有关多变量最值问题求解的一些常用方法,供大家参考.一、消元转化为单变量的函数例1已知x、y在区间(-2,2)内,且xy=-1,则函数u=
Each year the math entrance exam or competition will appear multivariate most value problems, such issues rich in content, wide range of knowledge, comprehensive, flexible solution is to examine the students to use basic knowledge, mathematical thinking and testing students thinking flexible Because of the large number of variables, students often find it difficult to find ways to solve problems and can do nothing but time-consuming. Here are some examples of commonly used methods for solving multivariable most value problems for your reference. First, the elimination of the conversion into a single variable function Example 1 Known x, y in the interval (-2,2), and xy = -1, the function u =