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

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Let \( \alpha \) and \( \beta \) be two real numbers such that \( \alpha+\beta=1 \) and \( \alpha \beta=-1 \). Let \( P_{n}=(\alpha)^{n}+(\beta)^{\mathrm{n}}, P_{n-1}=11 \) and \( P_{n+1}=29 \) for
P some integer \( n \geq 1 \). Then, the value of \( P_{\mathrm{n}}^{2} \) is:

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