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Algebra Level 4

Given the polynomial \(P(x)={2x}^{3}{-9x}^{2}+11x-84\) with roots \(a,b,c\).

We denote the values below:

\[ \begin{eqnarray} X &=& a^2 + b^2 + c^2 \\ Y &=& a^2 b + abc + a^2 c + b^2 a + b^2 c + abc + abc + c^2 a + bc^2 \\ Z &=& a^2 bc + b^2 ca + c^2 ab \\ \end{eqnarray} \]

Find \(X+Y+Z\).

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