Powers of 2014 , 2015 and 2016

Algebra Level 4

If x23x+1=0 x ^ 2 - 3x + 1 = 0 has roots α,β \alpha, \beta , then find the value of the expression below?

α2014+β2014+α2016+β2016α2015+β2015 \frac{ \alpha^ {2014} + \beta ^ { 2014 } + \alpha^{2016 } + \beta ^ { 2016 } } { \alpha ^ { 2015 } + \beta ^ { 2015 } }

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