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2016-2x-x-a-x-b-x-c-has-only-one-solution-a-lt-b-lt-c-a-b-c-Z-Find-the-lowest-value-of-c-




Question Number 153478 by naka3546 last updated on 07/Sep/21
2016−2x = ∣x−a∣+∣x−b∣+∣x−c∣   has  only  one  solution .  a<b<c    a,b,c ∈ Z  Find  the  lowest  value  of  c.
$$\mathrm{2016}−\mathrm{2}{x}\:=\:\mid{x}−{a}\mid+\mid{x}−{b}\mid+\mid{x}−{c}\mid\:\:\:{has}\:\:{only}\:\:{one}\:\:{solution}\:. \\ $$$${a}<{b}<{c}\:\: \\ $$$${a},{b},{c}\:\in\:\mathbb{Z} \\ $$$${Find}\:\:{the}\:\:{lowest}\:\:{value}\:\:{of}\:\:{c}. \\ $$

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