Devastating blow

Algebra Level 3

\[ \large x^{2011} + a_{1}x^{2010} + a_{2} x^{2009} +\ldots + a_{2010} +1\]

Given \(x_1 , x_2 , x_3 , \ldots , x_{2011}\) are the roots of the polynomial above and that \[\begin{eqnarray} y_1 &=& x_{1} \ x_{2} \cdots x_{10} \\ y_2 &=& x_{2} \ x_{3} \cdots x_{11} \\ y_3 &=& x_{3} \ x_{4} \cdots x_{12} \\ &\cdot& \\ &\cdot& \\ &\cdot& \\ y_{2011} &=& x_{2011}\ x_{1} \ x_{2} \cdots x_{9} \end{eqnarray} \]

Find the value of \( {{(y_1 \ y_2\ldots y_{2011})}^{2011}}^{2010}\).

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