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a-b-c-Z-a-b-3-b-c-3-1-Find-the-value-of-a-b-b-c-c-a-




Question Number 153512 by naka3546 last updated on 08/Sep/21
a,b,c  ∈  Z  ∣a−b∣^3  + ∣b−c∣^3  = 1  Find  the  value  of        ∣a−b∣ + ∣b−c∣ + ∣c−a∣
$${a},{b},{c}\:\:\in\:\:\mathbb{Z} \\ $$$$\mid{a}−{b}\mid^{\mathrm{3}} \:+\:\mid{b}−{c}\mid^{\mathrm{3}} \:=\:\mathrm{1} \\ $$$${Find}\:\:{the}\:\:{value}\:\:{of} \\ $$$$\:\:\:\:\:\:\mid{a}−{b}\mid\:+\:\mid{b}−{c}\mid\:+\:\mid{c}−{a}\mid \\ $$
Answered by MJS_new last updated on 08/Sep/21
for a, b, c ∈Z we have  a=b∧∣b_((a)) −c∣=1 ∨ ∣a−b_((c)) ∣=1∧b=c  ⇒  ∣a−b∣+∣b−c∣+∣c−a∣=2
$$\mathrm{for}\:{a},\:{b},\:{c}\:\in\mathbb{Z}\:\mathrm{we}\:\mathrm{have} \\ $$$${a}={b}\wedge\mid\underset{\left({a}\right)} {{b}}−{c}\mid=\mathrm{1}\:\vee\:\mid{a}−\underset{\left({c}\right)} {{b}}\mid=\mathrm{1}\wedge{b}={c} \\ $$$$\Rightarrow \\ $$$$\mid{a}−{b}\mid+\mid{b}−{c}\mid+\mid{c}−{a}\mid=\mathrm{2} \\ $$
Commented by naka3546 last updated on 08/Sep/21
thank  you, sir.
$${thank}\:\:{you},\:{sir}. \\ $$

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