Let \( \alpha \) and \( \beta \) be two real numbers such that \( \...

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Let \( \alpha \) and \( \beta \) be two real numbers such that \( \alpha+\beta=1 \)
\( \mathrm{P} \) and \( \alpha \beta=-1 \). Let \( p_{n}=(\alpha)^{n}+(\beta)^{n}, p_{n-1}=11 \) and

W \( p_{n+1}=29 \) for some integer \( n \geq 1 \). Then, the value of \( p_{n}^{2} \) is
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