Question

plz answer it guys l need help​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

$\sf{ \:If \: \omega \: \: is \: cube \: root \: of \: unity \: then \: }$

$\sf{ { \omega}^{3} = 1 \: \: and \: \: \:1 +\omega + {\omega}^{2} = 0\: }$

TO DETERMINE

${ \: ( 2 +\omega + {\omega}^{2}) \: }^{3} - { \:(1 - 3\omega + {\omega}^{2} )\: }^{3} = 65$

PROOF

${ \: ( 2 +\omega + {\omega}^{2}) \: }^{3} - { \:(1 - 3\omega + {\omega}^{2} )\: }^{3}$

$= { \: ( 1 + 1 +\omega + {\omega}^{2}) \: }^{3} - { \:(1 + \omega + {\omega}^{2} - 4 \omega)\: }^{3}$

$= { \: ( 1 +0)\: }^{3} - { \:(0 - 4 \omega)\: }^{3}$

$= 1 + 64 \: {\omega}^{3}$

$= 1 + 64$

$= 65$

Answer 2

your answer is 65...........