jika α dan β adalah akar−akar persamaan x^2 +x+1=0 maka nilai α^(2013) +β^(2301) =..... a.−2 c.0 e.2 b.−1 d.1


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Question Number 1050 by tera last updated on 23/May/15

$j i k a α d a n β a d a l a h a k a r - a k a r$ $p e r s a m a a n x^{2} + x + 1 = 0 m a k a$ $n i l a i α^{2013} + β^{2301} = . . . . .$ $a . - 2 c . 0 e . 2$ $b . - 1 d . 1$
	Answered by prakash jain last updated on 23/May/15

	$Root of equation are ω and ω^{2}$ $where 1, ω, ω^{2} are cube root of unity .$ $ω^{2013} + {(ω^{2})}^{2301} = {(ω^{3})}^{671} + {(ω^{3})}^{2 \times 767} = 1 + 1 = 2$
	Commented by prakash jain last updated on 23/May/15

	$Cube root of 1 are solutions of equation$ $x^{3} = 1$ $x^{3} - 1 = 0$ $(x - 1) (1 + x + x^{2}) = 0$ $1 + x + x^{2} g i v e s t w o s o l u t i o n s ω and ω^{2}$ $1 - x g i v e s o n e s o l u t i o n 1$ $The three solution are 1, w, w^{2}$
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