Let $α$ and $β$ be the roots of the equation $x^{2} - 3 x + 3 = 0$ .If $S$ is the algebraic sum of the coefficients and T is the term
independent of $x$ in ${((α + 1) x + \frac{(β + 1)}{x})}^{20}$ ,then :

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$T =^{20} C_{10} {.5}^{10}$

$T =^{20} C_{10} {.7}^{10}$

$S = 5^{20}$

$S = 3^{20}$

answer is A, D.

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Detailed Solution

$α a n d β b e t h e r o o t s o f t h e e q u a t i o n x^{2} - 3 x + 3 = 0$

$α + β = 3, α β = 3$

$S = {(α + 1 + β + 1)}^{20} = 5^{20}, T = {}^{20}C_{r} . {(α + 1)}^{20 - r} . x^{20 - r} . \frac{{(β + 1)}^{r}}{x^{r}}, r = 0 G i v e s, T = {}^{20}C_{10} . {(α β + α + β + 1)}^{10}$

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