Let $\alpha$ and $\beta$ be two real numbers such that $\alpha$ + $\beta$ = 1 and $\alpha$$\beta$ = $-$1. Let pn = ($\alpha$)n + ($\beta$)n, pn$-$1 = 11 and pn+1 = 29 for some integer n $ \ge $ 1. Then, the value of p$_n^2$ is ___________.

Question

Let $\alpha$ and $\beta$ be two real numbers such that $\alpha$ + $\beta$ = 1 and $\alpha$$\beta$ = $-$1. Let p_n = ($\alpha$)ⁿ + ($\beta$)ⁿ, p_n$-$1 = 11 and p_n+1 = 29 for some integer n $ \ge $ 1. Then, the value of p$_n^2$ is ___________.

Correct Answer

324

Solution

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