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有些数学问题,按某一对象分类讨论,可以防止错误现象产生.但分类讨论并非处处都是最有效的,对某些问题,分类讨论可能比较麻烦,若从“补集”的角度考虑问题,即从结论的反面去思考,得出反面结论后,结合集合性质A-=A,就容易得出正面的结论.这种思考方法可以达到化难为易、化繁为简、开拓解题思路的目的. 一、在三角中的应用 例1m为什么实数时,方程sin2x-sinx十m=0无实根. 分析本题若正面解,可由判别式小于零和|sinx|>1讨论出m的取值范围,但需要解无理不等式,运算量太大:也可以通过讨论二次函数的两种情况,列出关系式,这需要有一定的技巧,若从问题的反面考虑,可以避开这些麻烦.
Some mathematics problems can be classified and discussed according to a certain object, which can prevent the occurrence of erroneous phenomena. However, the classification discussion is not always the most effective. For some problems, the classification and discussion may be too much trouble. If you consider the problem from the perspective of “supplement”, That is to say, from the opposite side of the conclusion, after the negative conclusion is drawn, combining the collection property A-=A, it is easy to draw a positive conclusion. This kind of thinking method can achieve the difficulty, the complexity, the simplicity, and the problem solving. Objectives 1. First, in the application of the triangle 1m why the real number, the equation sin2x-sinx ten m = 0 no real roots. Analysis of this question if the positive solution, by the discriminant less than zero and | sinx |> 1 to discuss the value of m Range, but need to solve irrational inequality, too much calculation: You can also discuss the two conditions of the quadratic function, listed relations, which requires certain skills, if you consider from the wrong side of the problem, you can avoid these problems.