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Mathematics · 2020
JEE Main · 7 January 2020, Shift 2 · Q51
Let α and β be the roots of the equation x^2-x-1=0. If p_k =(α)^k +(β)^k, k ≥ 1, then which one of the following statements is not true?
Let $\displaystyle \alpha$ and $\displaystyle \beta$ be the roots of the equation $\displaystyle x^2-x-1=0$. If $\displaystyle \mathrm{p}_{\mathrm{k}}=(\alpha)^{\mathrm{k}}+(\beta)^{\mathrm{k}}, \mathrm{k} \geqslant 1$, then which one of the following statements is not true ?
Official answer
(4)
$\displaystyle \mathrm{p}_5=\mathrm{p}_2 \cdot \mathrm{p}_3$
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JEE Main 2020 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.