Polynomial Equation Under The Moon Light

Algebra Level 4

If we know that \(x^6 + x^5 + x^4 + x^3 + x^2 +x + 1 = 0\)

And given that \[\begin{eqnarray} a &=& \left(\frac{1}{x} + x \right)\left(\frac{1}{x} +x + 2\right)\left(\frac{1}{x} + x - 1\right) \\ b &=& \left(\frac{1}{x} + x \right)^3 +\left (\frac{1}{x} +x - 1 \right)^2 \end{eqnarray} \]

What is the value of \(a+b\)?

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