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函数与方程有着密切的联系,在解决某些数学问题时,可以通过适当的构造,把问题转化为研究函数与方程来解决。下面,笔者结合例题说明如何运用函数与方程的思想方法来分析和解决问题。例1设不等式2x-1>(x~2-1)m对满足|m|≤2的一切实数m恒成立,求实数x的取值范围。分析:由于常见的思维定势,易把本题看成关于x的不等式进行分类讨论。然而,若变换角度,以m
Functions and equations are closely linked. When solving certain mathematical problems, they can be solved by transforming the problems into research functions and equations through proper construction. The following, the author combines examples to illustrate how to use functions and equations of thought to analyze and solve problems. Example 1 Let inequation 2x-1> (x ~ 2-1) m satisfy all | m | ≤2 all real constant m holds, find the real number x range of values. Analysis: Due to the common tendency of thinking, it is easy to think of this question as a classification discussion about the inequalities of x. However, if we change the angle in m