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配方法是解决数学问题的一个重要方法,应用极其广泛,特别是在解一元二次(或可化为一元二次)不等式中,不要记许多公式,解题过程简单,方法固定,便于掌握。其理论依据是:若a>0,则 1)|x|a←→x~2>a~2。例1 解以下不等式: 1)x~2+21≤10x 解把原不等式化为x~2-10x+5~2≤4→(x-5)~2≤2~2→|x-5|≤2→-2≤x-5≤2→3≤x≤7即得原不等式解集是〔3,7〕
Matching method is an important method to solve mathematics problems. It is extremely widely used, especially in the solution of a one-time quadratic (or can be converted into a quadratic) inequality, do not remember many formulas, the problem-solving process is simple, the method is fixed, easy to grasp. The theoretical basis is: if a>0, then 1)|x|a←→x~2>a~2. Example 1 Solution of the following inequality: 1) The solution of x~2+21≤10x turns the original inequality into x~2-10x+5~2≤4→(x-5)~2≤2~2→|x-5| ≤2→-2≤x-5≤2→3≤x≤7 The solution set of the original inequality is [3,7]