Bashing roots

Algebra Level 3

if \(a\) and \(b\) are roots of \(x^2 - 3x + 1 = 0\) then find the value of \[ \large \frac{a^{2014} + b^{2014} + a^{2016} + b^{2016}}{a^{2015} + b^{2015}}.\]

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