x^2 +x+1=0 x^(92) =?


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Question Number 186636 by Noorzai last updated on 07/Feb/23

$x^{2} + x + 1 = 0$ $x^{92} = ?$
Commented by Rasheed.Sindhi last updated on 07/Feb/23

$x^{92} = ω, ω^{2} w h e r e ω i s c o m p l e x c u b e r o o t$ $o f u n i t y .$
Commented by Noorzai last updated on 07/Feb/23

$G i v e a n e x p l a n a t i o n$
	Answered by mr W last updated on 07/Feb/23

	$\frac{1}{x^{2}} + \frac{1}{x} + 1 = 0$ $\Rightarrow \frac{1}{x} = \frac{- 1 \pm \sqrt{3} i}{2}$ $(x - 1) (x^{2} + x + 1) = 0$ $x^{3} - 1 = 0$ $x^{3} = 1$ $x^{92} = \frac{x^{93}}{x} = \frac{{(x^{3})}^{31}}{x} = \frac{1}{x} = \frac{- 1 \pm \sqrt{3} i}{2}$
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