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在学习二次根式知识的过程中,我们会经常遇到有关的运算问题,求解此类问题时,如果能够掌握一些比较常用的方法和技巧,不仅可以简化解题过程,而且可以快速正确地求解.一、巧用定义例1求(1-a)~(1/2)-(a-1)~(1/2)+2012a的值.解:由1-a≥0,得a≤1;又a-1≥0,得a≥1.从而可知a=1.故原式=0-0+2012×1=2012.二、逆用公式例2化简3~(1/2)+5~(1/2)/(4~(1/2)+15~(1/2))~(1/2)解:显而易见原式大于零,故有
In the process of learning the root-mean-square knowledge, we often encounter the related computing problems. When we solve such problems, if we can learn some commonly used methods and techniques, we can not only simplify the problem-solving process, but also solve it quickly and correctly First, use the definition example 1 to find the values of (1-a) ~ (1/2) - (a-1) ~ (1/2) + 2012a Solution: from 1-a≥0, we get a≤1 ; And a-1 ≥ 0, to be a ≥ 1. Thus we can see that a = 1. Therefore, the original = 0-0 + 2012 × 1 = 2012. Inverse formula Example 2 Simplified 3 ~ (1/2) + 5 ~ (1/2) / (4 ~ (1/2) + 15 ~ (1/2)) ~ (1/2) Solution: Obviously the original is greater than zero,