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运用基本不等式求最值是高考中常见的一种问题,由于基本不等式a~2+b~2≥2ab(a,b∈R),a+b≥2 ab~(1/2)(a>0,b>0)具有明显的结构特征(两数的平方和、和与积),因而解这类问题的关键是,先仔细观察已知和目标式子的结构形式,再根据结构形式的特征选用合理的方法:出现平方和、和与积三种结构时,可合理截取不等式段;遇见多元问题时,想减元或轮换对称结构;要求积最大值时,找和定,要求和最小值时,找积定.
The use of basic inequality to find the most value is a common problem in college entrance examination, as the basic inequalities a ~ 2 + b ~ 2 ≥ 2ab (a, b∈R), a + b ≥ 2 ab ~ (1/2) (a> 0, b> 0) has obvious structural features (sum of squares and sum of two numbers). Therefore, the key to solving this kind of problem is to carefully observe the structural forms of the known and objective formulas, and then according to the structural form Feature selection of a reasonable method: the emergence of the sum of squares, and product of three kinds of structure, it can reasonably intercept the inequality segment; meet multiple problems, want to reduce the element or rotation symmetry structure; Value, find the product set.