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增补法是数学解题中的一种创造性思维方法,通过增补性的构作,把题情中的隐含信息显露出来,尽快地沟通结论与条件间的逻辑关系,为我们开辟一条易于发现的解题思路.下面提供一些常见的增补性的措施.1.增补条件解某些对称性问题时,可通过增补条件来扩大思维领域,创造良好的解题氛围,从而增进解题的灵活性.例1 求不定方程1/x+1/y+1/z=7/8的正整数解.
Supplementary method is a creative thinking method in mathematics problem solving. Through the construction of supplements, the hidden information in the question is exposed, and the logical relationship between conclusions and conditions is communicated as soon as possible, opening up an easily discoverable Problem-solving ideas. Here are some common supplementary measures. 1. Supplementary conditions When solving certain symmetry problems, you can expand the field of thinking by adding conditions to create a good problem-solving atmosphere, thereby increasing the flexibility of problem solving. Example 1 Find the positive integer solution of the indefinite equation 1/x+1/y+1/z=7/8.