Submitted by Francis Gerard Magtibay

Algebra Level 4

Suppose x+1x=433x+ \frac {1}{x}= \frac{4 \sqrt {3}}{3} . Then x10+1x10=a+bc x^{10}+ \frac {1}{x^{10}}=a+ \frac {b}{c} , where a a , b b and c c are positive integers, bc\frac{b}{c} is less than 11, and b b and c c are coprime. Find a+b+c a+b+c .

This problem is from the UP Math Wizard 2010.

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