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Algebra Level 5

(x+1x)2+(x2+1x2)2+(x3+1x3)2++(x2016+1x2016)2\large \left(x + \frac{1}{x}\right)^2 + \left(x^2 + \frac{1}{x^2}\right)^2 + \left(x^3 + \frac{1}{x^3}\right)^2 + \cdots + \left(x^{2016} + \frac{1}{x^{2016}}\right)^2

If x2+x+1=0{ x }^{ 2 }+x+1=0, evaluate the expression above.

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