A right substitution

Algebra Level 5

\[ \left ( x + \frac 1 x \right )^2 + \left ( x^2 + \frac 1 {x^2} \right )^2 + \ldots + \left ( x^{1000} + \frac 1 {x^{1000}} \right )^2 \]

What is the value of the expression above if \(x^2 + x+ 1 = 0 \)?

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