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在解一些数学问题时,针对题中一个式子f的结构特征,配上一个与f有内在联系的式子f_1(称为f的对偶式),凭籍f与f_1之间的一种或两种运算,便能促使问题的转化和解决。这种解数学题的思维策略,我们称为“配偶”。运用配偶策略解数学题的过程归为: 善于运用配偶策略来处理问题,乃是一项重要的数学基本功! 运用配偶策略解题的关键在于: (1)已知f,能确定出f的对偶式f_1; (2)选择f与f_1之间的适当运算。关于(1),这里仅给出常用的如下配偶式:
In solving some mathematical problems, for the structural features of a formula f in the problem, coupled with an equation f_1 which is intrinsically linked to f (called the duality of f), the relationship between f and f_1 Two kinds of calculations can prompt the transformation and resolution of problems. This kind of thinking strategy for solving math problems is called “spouse.” The process of using spouse strategies to solve math problems is classified as: Good at using spouse strategies to deal with problems, but it is an important basic skill of mathematics! The key to using spouse strategies to solve problems is: (1) Known f can determine the duality of f. Formula f_1; (2) Choose the appropriate operation between f and f_1. Regarding (1), only the commonly used spouses are given here: