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If $x ^ 2 - 3x + 1 = 0$ has roots $\alpha, \beta$, then find the value of the expression below?

$\frac{ \alpha^ {2014} + \beta ^ { 2014 } + \alpha^{2016 } + \beta ^ { 2016 } } { \alpha ^ { 2015 } + \beta ^ { 2015 } }$

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