TR-MO-R1 2012 Problem 23

$a$ , $b$ , $c$ gerçel sayıları $x^3-3x+1=0$ denkleminin farklı kökleri ise, $a^8+b^8+c^8$ nedir?

a) $156$ b) $171$ c) $180$ d) $186$ e) $201$

Official text Turkish Mathematical Olympiad, first round 2012 official paper, page 7. Quoted with source.

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