Five roots

Algebra Level 5

The equation \(x^5-2x^4-1=0\) has five complex roots \(r_1, r_2, r_3, r_4, r_5\). Find the value of \[\frac{1}{r_1^8}+\frac{1}{r_2^8}+\frac{1}{r_3^8}+\frac{1}{r_4^8}+\frac{1}{r_5^8}. \]

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