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数学解题中,虽然掌握定理、公式、法则是关键,但由于习题的类型较多,特点不一,技巧也不可忽视。比如,有一类习题的结论是“至少”问题,按常规解法,要分多种简单的问题讨论,其解法繁杂且难,若运用一些技巧,不仅可以提高解题速度,而且还简单明了,下面就此介绍三则,望能对解这类问题有所启示。一、若A_1·A_2·A_3·…·A_n=0,则A_1,A_2,A_3,…,A_n中至少有一个为零。例1 一个凸四边形被它的两条对角线分成四个三角形,以该四边形的一组对边为边的两个三角形面积的平方和与以另一组对边为边的两个三角形面积的平方和相等,求证:至少
In mathematics problem solving, though mastering theorems, formulas, and rules is the key, due to the types of exercises and their different characteristics, skills cannot be ignored. For example, the conclusion of one type of exercise is the “at least” problem. According to the conventional method of solution, there are many simple problems to discuss. Its solution is complicated and difficult. If you use some techniques, you can not only improve the speed of problem solving, but also make it simple and straightforward. Introducing three of them in this regard hopes to inspire the solution to this type of problem. 1. If A_1·A_2·A_3·...·A_n=0, at least one of A_1, A_2, A_3,..., A_n is zero. Example 1 A convex quadrilateral is divided into four triangles by its two diagonals. The sum of squares of the area of two triangles whose sides are the sides of the quadrilateral, and the area of two triangles with the edges of the other set of edges. The sum of squares is equal, verify: at least