Newton's Sums, here?

Algebra Level 5

\[\large x^3 + 2x^2 - 3x - 1 = 0\]

If \(a,b \text{ & } c \) are the roots of this equation, find the value of \(\displaystyle \sum_{\text{cyc}} \dfrac{1}{a^3} \).


Note:

\(\displaystyle \sum_{\text{cyc}} \) denotes cyclic summation.

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