Sum of Powers of Roots (Jee Mains)

Algebra and Representation of Complex Numbers

Medium

Sum of Powers of Roots

If x² + x + 1 = 0, then the value of
${\left( {x + \frac{1}{x}} \right)^4} + {\left( {{x^2} + \frac{1}{{{x^2}}}} \right)^4} + {\left( {{x^3} + \frac{1}{{{x^3}}}} \right)^4} + ... + {\left( {{x^{25}} + \frac{1}{{{x^{25}}}}} \right)^4}$ is :

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