# Groups of Reciprocal Friends

Algebra Level 4

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

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

×