Newtons Inverse Roots?

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 \[\frac{1}{r_1^9}+\frac{1}{r_2^9}+\frac{1}{r_3^9}+\frac{1}{r_4^9}+\frac{1}{r_5^9}. \]

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