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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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by Sarthak Rath

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