Submitted by Francis Gerard Magtibay

Algebra Level 4

Suppose \(x+ \frac {1}{x}= \frac{4 \sqrt {3}}{3} \). Then \( x^{10}+ \frac {1}{x^{10}}=a+ \frac {b}{c} \), where \( a \), \( b \) and \( c \) are positive integers, \(\frac{b}{c}\) is less than \(1\), and \( b \) and \( c \) are coprime. Find \( a+b+c \).

This problem is from the UP Math Wizard 2010.

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