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同学们在解需要分类讨论的问题时,最常犯的错误是漏解.解这类问题时如果分类得当,可将所有正确结果一网打尽,下面举例说明.一、线段问题例1己知线段AB=8,在直线AB上有一点C,且BC=4,M是线段AC的中点,求线段AM的长.解析:点C可能在线段AB上,也可能在线段AB的延长线上,因此要分类讨论.(1)当点C在线段AB上时,如图1.因为M是线段AC的中点,所以AM=1/2AC=
The most common mistakes made by students when solving the problems that need to be categorized are the omissions. If the problems are classified properly, all the correct results can be exhausted, as an example below. = 8, there is a point C on the straight line AB, and BC = 4, M is the midpoint of the line segment AC, and the length of the line segment AM is required. Analysis: Point C may be on the line segment AB or the extension line of the line segment AB, Therefore, to be classified discussion (1) when the point C on the AB segment, shown in Figure 1. Because M is the midpoint of the line segment AC, so AM = 1 / 2AC =