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Let $\alpha$ and $\beta$ be the roots of the equation, 5x2 + 6x – 2 = 0. If Sn = $\alpha$n + $\beta$n, n = 1, 2, 3,....., then :

(1) 6S6 + 5S5 = 2S4

(2) 5S6 + 6S5 = 2S4

(3) 5S6 + 6S5 + 2S4 = 0

(4) 6S6 + 5S5 + 2S4 = 0

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Ans. (2) 5S6 + 6S5 = 2S4

Sol. 5$\alpha$2 + 6$\alpha$ = 2

5S6 + 6S5 = $\alpha$4(5$\alpha$2 + 6$\alpha$) + $\beta$4(5$\beta$2 + 6$\beta$)

= 2($\alpha$4 + $\beta$4) = 2S4

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