Raised to 5and 9

Algebra Level 5

If \(r_{1}\),\(r_{2}\),\(r_{3}\),\(r_{4}\),\(r_{5}\) are the complex roots of the equation \(x^{5}-3x^{4}-1=0\) . Find the value of

\[ \large \frac{1}{r_{1}^{9}}+\frac{1}{r_{2}^{9}}+\frac{1}{r_{3}^{9}}+\frac{1}{r_{4}^{9}}+\frac{1}{r_{5}^{9}}\]

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