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我们在解数学题的过程中,有时会遇到解题思路受阻的情况,感觉缺少什么条件.此时若能加上某个条件,则思路豁然畅通,解题可以顺利进行.以下有六种为解题增加条件的常用方法.一、反证法反证法被誉为“数学家最精良的武器之一”.用反证法证明一个命题时,我们从结论的反面入手,先假设结论的反面成立,增加了条件,然后由此结合题设、公理、定义等进行推理,导出矛盾,从而肯定原命题成立.例1已知函数f(x)=2x2+mx+n,求证:|f(1)|,|f(2)|,|f(3)|中至少有一个不小于1.证明假设原结论不成立,即|f(1)|,|f(2)|,|f(3)|都小于1.
In the process of solving mathematical problems, we sometimes encounter problem-solving ideas hindered the situation, the lack of any feeling of the conditions at this time if you add a condition, then suddenly clear ideas, problem-solving can proceed smoothly. There are six kinds of A common method to solve the problem of increasing conditions.An anti-card law anti-card law known as “mathematicians with one of the most sophisticated weapons. ” Proof of a proposition by proof, we start from the opposite of the conclusion, the first assumption that the opposite of the establishment of the conclusion, (1) Given the function f (x) = 2x2 + mx + n, prove: | f (1) | f (2) |, | f (3) | is not less than 1. Proof It is assumed that the original conclusion does not hold, that is, | f All less than one.