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构造法就是根据题设条件或结论所具有的特征和性质,构造满足条件或结论的数学对象,并借助该对象来解决数学问题的思想方法。运用构造法解决问题,关键在于构造什么和怎么构造。充分地挖掘题设与结论的内在联系,把问题与某个熟知的概念、公式、定理、图形联系起来,构造恰当数学模型。一、构造几何图形,巧解方程问题例1.已知x-1+x-5=4,则x的取值范围是.分析:根据绝对值的几何意义可知x-1+x-5=4表示数轴
Constructive method is to construct the mathematical object that satisfies the conditions or conclusion according to the characteristics and nature of the conditions or conclusion of the problem, and use the object to solve the thinking method of the mathematical problem. The key is to construct what and how to construct. Fully excavate the internal connection between the problem setting and the conclusion, and connect the problem with a well-known concept, formula, theorem and graph to construct the appropriate mathematical model. First, the construction of geometric figures, solving equations equation problem 1. Known x-1 + x-5 = 4, then the range of x is. Analysis: According to the geometric meanings of the absolute value of x-1 + x-5 = 4 indicates the number of axes