If a and ẞ roots of x ^ 2 - 2x + 4 = 0 prove that alpha ^ n + beta ^ n = 2 ^ (n + 1) * cos((n*pi)/3)

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If `alpha` and `beta` are the roots of the equation `x^2-2x+4=0`, prove that `alpha^n+beta^n=2^... If `alpha` and `beta` are the roots of the equation `x^2-2x+4=0`, prove that `alpha^n+beta^n=2^...
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