Newton's Sums, here?

Algebra Level 5

x3+2x2−3x−1=0\large x^3 + 2x^2 - 3x - 1 = 0

If a,b & ca,b \text{ \& } c are the roots of this equation, find the value of ∑cyc1a3\displaystyle \sum_{\text{cyc}} \dfrac{1}{a^3} .

Note:

∑cyc\displaystyle \sum_{\text{cyc}} denotes cyclic summation.

Vishwak Srinivasan by Vishwak Srinivasan
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