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解数学题,不仅要注意积累经验,总结方法;还要在原有经验和方法的基础上,敢于冲破思维定势的束缚,开扩思路,进行合理的联想,以找到新的解法。这样作,有时还可发现新的知识和结论,对培养创造性思维和探究能力很有好处。联想的途径和方法很多,本文仅从两个方面略加探讨。一、注意题目特点,联想解题方法。有些题目,内容或形式与某一定理或公式相合,就可变通使用这些知识来帮助解决。例1 设a,b,c为实数,求证a,b,c都是正数的充要条件是;①a+b+c>0;②ab+bc+ca>0;③abc>0。证必要性显然,下面证充分性。
Solve mathematics problems, not only to pay attention to the accumulation of experience, summing up methods; but also based on the original experience and methods, dare to break through the shackles of the mindset, open up ideas, make reasonable associations to find new solutions. In doing so, new knowledge and conclusions can sometimes be found, which is good for developing creative thinking and exploring capabilities. There are many ways and methods of association, this article only slightly discusses from two aspects. First, pay attention to the characteristics of the problem, Lenovo problem solving method. Some topics, contents, or forms fit a certain theorem or formula, and they can be used to help solve the problem. Example 1 Let a, b, and c be real numbers. The necessary and sufficient condition for verifying that a, b, and c are all positive is: 1a+b+c>0; 2ab+bc+ca>0; 3abc>0. The evidentiary necessity is clearly evident below.