Groups of Reciprocal Friends

Algebra Level 4

(x+1x)2+(x2+1x2)2++(x27+1x27)2\left( x + \frac{1}{x} \right)^2 + \left( x^2 + \frac{1}{x^2} \right)^2 + \cdots + \left( x^{27} + \frac{1}{x^{27}} \right)^2

If xx is a complex number satisfying x2+x+1=0x^2 + x + 1 = 0, determine the value of the expression above.


Source: Trinity University
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