Let $\alpha$ and $\beta$ be the roots of the equation $\mathrm{x}^{2}-\mathrm{x}-1=0 .$ If $\mathrm{p}_{\mathrm{k}}=(\alpha)^{\mathrm{k}}+(\beta)^{\mathrm{k}}, \mathrm{k} \geq 1,$ then which one of the following statements is not true?

  • [JEE MAIN 2020]
  • A

    $\left(p_{1}+p_{2}+p_{3}+p_{4}+p_{5}\right)=26$

  • B

    $\mathrm{p}_{5}=11$

  • C

    $\mathrm{p}_{3}=\mathrm{p}_{5}-\mathrm{p}_{4}$

  • D

    $\mathrm{p}_{5}=\mathrm{p}_{2} \cdot \mathrm{p}_{3}$

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