Mathematics · 2022
JEE Main · 29 July 2022, Shift 2 · Q22
Let α, β(α>β) be the roots of the quadratic equation x^2-x-4=0. If P_n=α^n-β^n, n ∈ N, then (P_15 P_16-P_14 P_16-P_15^2+P_14 P_15)/(P_13 P_14) is…
Let $\displaystyle \alpha, \beta(\alpha>\beta)$ be the roots of the quadratic equation $\displaystyle x^2-x-4=0$. If $\displaystyle P_n=\alpha^n-\beta^n$, $\displaystyle n \in \mathbb{N}$, then $\displaystyle \frac{P_{15} P_{16}-P_{14} P_{16}-P_{15}^2+P_{14} P_{15}}{P_{13} P_{14}}$ is equal to \_\_\_\_.
Official answer
16
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JEE Main 2022 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.