Let \( \alpha \) and \( \beta \) be the roots of the equation \( x^...

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Let \( \alpha \) and \( \beta \) be the roots of the equation \( x^{2}-x-1=0 \). If \( p_{k}=(\alpha)^{k}+(\beta)^{k}, k \geq 1 \), then which of the following
P statements is not true? [JEE Main-2020 (January)]

W.
(1) \( \mathrm{p}_{5}=\mathrm{p}_{2} \cdot \mathrm{p}_{3} \)
(2) \( \left(\mathrm{p}_{1}+\mathrm{p}_{2}+\mathrm{p}_{3}+\mathrm{p}_{4}+\mathrm{p}_{5}\right)=26 \)
(3) \( \mathrm{p}_{3}=\mathrm{p}_{5}-\mathrm{p}_{4} \)
(4) \( \mathrm{p}_{5}=11 \)
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