If $\alpha $ and $\beta $ are the roots of the equation ${x^2} - x + 1 = 0,$ then ${\alpha ^{2009}} + {\beta ^{2009}} = $ - DASH

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Question

If $\alpha $ and $\beta $ are the roots of the equation ${x^2} - x + 1 = 0,$ then ${\alpha ^{2009}} + {\beta ^{2009}} = $

$\, - 1$

$\, 1$

$\, 2$

$\, - 2$

Solution

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