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From module Algebra Basics
Suppose aaa, bbb, and ccc are nonzero real numbers, and a+b+c=0a+b+c=0a+b+c=0. What are the possible value(s) for a∣a∣+b∣b∣+c∣c∣+abc∣abc∣\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}+\frac{abc}{|abc|}∣a∣a+∣b∣b+∣c∣c+∣abc∣abc?
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