Powers of 2014 , 2015 and 2016
Algebra
Level
4
If \( x ^ 2 - 3x + 1 = 0 \) has roots \( \alpha, \beta \), then find the value of the expression below?
\[ \frac{ \alpha^ {2014} + \beta ^ { 2014 } + \alpha^{2016 } + \beta ^ { 2016 } } { \alpha ^ { 2015 } + \beta ^ { 2015 } } \]
by
Tanmay Sinha