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在高中经常遇到不等式恒成立问题。恒成立问题涉及一次函数、二次函数的性质、图象,渗透着换元、化归、数形结合、函数与方程等思想方法,恒成立问题解题的基本思路是:根据已知条件将恒成立问题向基本类型转化,如何正确选用解题方法求解.下面通过对具体问题的分析来说明“恒成立”问题.一、识清变量与参量如:若不等式2x-1>m(x2-1)对一切m∈(-2,2)都成立,求实数x的取值范围.其中m是变量,x是参量.
Often encountered in high school inequality established problem. The problem of constant set-up involves one-time functions, the nature of quadratic functions, images, infiltration of concepts such as commutation, regression, combination of numbers and forms, functions and equations. The basic idea of constant problem-solving is that according to known conditions Constantly established problem to the basic type conversion, how to correctly solve the problem-solving method. The following specific problems through the analysis to illustrate “Constantly established ” First, to identify variables and parameters such as: If the inequality 2x-1> m ( x2-1) holds true for all m∈ (-2,2), seeking the range of real numbers x, where m is a variable and x is a parameter.