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根据绝对值的运算性质,|a+b|≤|a|+|b|当且仅当 ab≥0时等号成立.利用这一简单性质解一类绝对值方程,可避免繁琐的分类讨论,使问题得到巧解.例1 已知|2m-11|=|m-3|+|m-8|,求 m的值.(北京师院出版社《初中数学竞赛专题精讲》P_(43)例4)
According to the operation property of the absolute value, |a+b|≤|a|+|b| holds if and only if ab≥0. Using this simple property to solve a class of absolute value equation avoids tedious classification discussions The problem is solved cleverly. Example 1 Known|2m-11|=|m-3|+|m-8|, find the value of m. (Beijing Normal University Press “Junior Mathematics Competition”) P_ ( 43) Example 4)