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How to explain?

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楼主

发表于 2005-2-23 01:13:58 | 显示全部楼层

Or even infinitely many.

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沙发

发表于 2005-2-23 02:13:59 | 显示全部楼层

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5 主题	155 帖子	1115 积分

板凳

发表于 2005-2-23 05:00:20 | 显示全部楼层

Infinitely many:

|x+1|+|x-1|=2. Obviously, [-1, 1] is the solution set.

Three solutions:

Well, I do not have one example. Actually I do not think we can have one. Cause

f(x)=|ax+b|+|cx+d|+...+|mx+n| is convex..... Therefore, if there are only a finite number of solutions, then there are 2, 1, or zero solutions.

Need to check again though.

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