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______.

Step-by-step solution

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                                                       +                                         &#1