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在数学解题中常会退到这种情形:若按一般的常规思路去解题会显得相当繁杂,或者是觉得无从下手,但是将问题作一适当地转换,就可能绝处逢生,得到较为巧妙的解法。本文将讨论这种转换思想之一,即逆向思维的方法。一、逆用法则、公式例 1 化简 (6~(1/2)+4 3~(1/2)+3 2~(1/2)/(6~(1/2)+3~(1/2))(3~(1/2)+2~(1/2)) (1986年北京数学竞赛题) 分析:直接分母有理化是很繁琐的。若
In mathematics problem solving, one often retreats to this situation: If the general routine is used to solve the problem, it will be rather complicated, or it may be impossible to start the problem. However, if the problem is properly converted, it may come to the fore and get better results. Clever solution. This article will discuss one of the conversion ideas, namely the method of reverse thinking. First, inverse usage, formula example 1 Simplification (6~(1/2)+4 3~(1/2)+3 2~(1/2)/(6~(1/2)+3~( 1/2))(3~(1/2)+2~(1/2)) (1986 Beijing Mathematical Contest) Analysis: The direct denominator’s rationalization is very tedious.