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If $\alpha, \beta$ are the roots of the equation $x^2-2 x+4=0$ and for any $n \in \mathrm{N}, \alpha^n+\beta^n=k \cos \frac{n \pi}{3}$ then $k=$
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The correct answer is:
$2^{n+1}$
No solution. Refer to answer key.
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