Bashing roots

Algebra Level 3

if aa and bb are roots of x23x+1=0x^2 - 3x + 1 = 0 then find the value of a2014+b2014+a2016+b2016a2015+b2015. \large \frac{a^{2014} + b^{2014} + a^{2016} + b^{2016}}{a^{2015} + b^{2015}}.

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