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 :

Question

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

5S₆ + 6S₅ = 2S₄

5S₆ + 6S₅ + 2S₄ = 0

6S₆ + 5S₅ + 2S₄ = 0

6S₆ + 5S₅ = 2S₄

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