Not Newton's Sum
Algebra
Level
4
Consider the cubic equation \( 245x^3 - 287x^2 + 99x - 9 = 0 \) with roots \( \alpha , \beta , \gamma \). If
\[ \displaystyle\sum_{r=0}^{\infty} \left ( \alpha^{r} + \beta^{r} + \gamma^{r} \right ) \]
is of the form \( \frac {m}{n} \), where \(m\) and \(n\) are coprime positive integers, what is value of \( \frac {m}{n+1} \)?
by
Kunal Joshi