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利用不等式求最值,主要依据以下基本不等式及其变形:a~2+b~2≥2ab,(a+b)/2≥(ab)~(1/2)(a>0,b>0).在使用过程中必须满足“一正二定三相等”三个条件,缺一不可.在使用过程中,为了满足以上三个条件,往往要对所给的代数式进行适当的变形,通常称为“凑型”.1.加减凑型例11求函数y=x+1+1/(x-2)(x>2)的最小值.解:因为x>2,所以x-2>0.
The use of inequalities to find the most value, mainly based on the following basic inequalities and their deformation: a ~ 2 + b ~ 2 ≥ 2ab, (a + b) / 2 ≥ (ab) ) In the course of the use must meet “a positive two fixed three equal ” three conditions, one is indispensable.In the course of using, in order to meet the above three conditions, often to give the appropriate algebraic deformation, usually Is called “Coarse ” 1. Addition and Subtraction Example 11 Find the minimum value of the function y = x + 1 + 1 / (x-2) (x> 2) Solution: Since x> 2, x -2> 0.