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