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在数学研究中,使一种研究对象在一定条件下转化为另一种研究对象的思想称为转化思想。解题其实就是对问题进行转化,使之逐步成为已解决过的问题的模式,沟通条件与结论的联系的过程。即达到化繁为简、化难为易的目的。等价转化是利用等价原理(如充要条件、逆否命题与原命题的关系)进行转化。只有对原问题等价转化,所得到的解才是原问题的解。等价转化思想和函数思想、数形结合思想、分类讨论思想一样是近几年来高考强调考查的重要数学思想,在复习中必须引起高度重视。下面将着重阐述对命题进行等价转化的一些常用策略及等价转化的途径和方法,以飨读者。
In mathematics research, the idea of transforming a research object into another research object under certain conditions is called transformative thinking. The problem-solving problem is actually the transformation of the problem, so that it gradually becomes the model of the problem that has been solved and the process of linking the conditions and conclusions. That is to achieve the goal of simplifying and simplifying and making things difficult. Equivalent transformation is the use of the equivalence principle (such as the necessary and sufficient conditions, the relationship between the inverse proposition and the original proposition). Only the equivalent transformation of the original problem, the solution is the solution to the original problem. Equivalent transformation ideas and function ideas, combined ideas of number and shape, and categorized discussion ideas are the important mathematics ideas that the college entrance examination emphasizes on examination in recent years and must be highly valued during review. The following will focus on some commonly used strategies for the equivalent transformation of propositions and the equivalent transformation of the ways and methods to readers.