Let α and β be two real numbers such that α + β = 1 and α β = - 1 . Let p n = α n + β n , p n - 1 = 11 and p n + 1 = 29 for some integer n ⩾ 1 . Then, the value of p n 2 is______.

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x 2 - x - 1 = 0 roots = α , β α 2 - α - 1 = 0 ⇒ α n + 1 = α n + α n - 1 β 2 - β - 1 = 0 ⇒ β n + 1 = β n + β n - 1 + p n + 1 = p n + p n - 1 29 = p n + 11 p n = 18 p n 2 = 324

Mathematics - Quadratic Equation Question with Solution | TestHub

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