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Let a, b, c be nonzero real numbers.  Find all possible values of \(\displaystyle \frac{a}{|a|} + \frac{b}{|b|} + \frac{c}{|c|} + \frac{abc}{|abc|}\)

 May 14, 2020
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Each one of the individual terms will have either a value of 1 or -1.

If a, b, and c are all positive, then so is abc, so the sum will be 1 + 1 + 1 + 1  =  4

If one of a, b, and c is negative, then so is abc, so the sum will be 0.

If two of a, b, and c are negative, then abc is positive, so the sum will be zero.

If all three are negative, then so is abc, so the sum will be -4.

 

The possible values are -4, 0, or 4.

 May 14, 2020

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