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Let α,β,γ are roots of ax3+bx2+cx+d=0 then \sum{(\frac{\alpha +1}{\alpha -1})(\frac{\beta +1}{\beta -1})}=?
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3 Answers
62\texttt{First note :} a(x+1)^{3}+b(x+1)^{2}+c(x+1)+d \texttt{ will have roots \alpha-1, \beta - 1 and \gamma - 1}
\text{given summation is same as } \sum{\left\{1+\frac{1}{\alpha -1}+\frac{1}{\beta -1}+\frac{1}{(\alpha -1)(\beta -1)} \right\}}
Now can you solve this?