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不等式恒成立问题,参变量潜在约束影响,参数出现增加了问题的难度,且不易理清思路.本文针对这个问题总结以下几种方法,希望对大家有所帮助。第一招:分类讨论法例1:若不等式(a-2)x2+2(a-2)x-4<0对一切x∈R恒成立,求a的取值范围.分析:本题关于x的函数可能为一次函数,可能为二次函数,须分两种情况讨论.【解析】:当a-2=0时,f(x)=-4<0恒成立,
Inequality constant established problems, parametric variables influence the potential constraints, the parameters appear to increase the difficulty of the problem, and difficult to sort out the train of thought.This paper summarizes the following methods to solve this problem, I hope everyone is helpful. The first one: Category discussion Law 1: If the inequality (a-2) x2 +2 (a-2) x-4 <0 for all x∈R holds established, find a range of values. Analysis: This question on the x Function may be a function, may be a quadratic function, to be divided into two cases to be discussed. [Resolve]: When a-2 = 0, f (x) = - 4 <0 holds,