Mathematics · 2021
JEE Main · 25 July 2021, Shift 1 · Q90
If α, β are roots of the equation x^2+5(√ 2 ) x+10=0, α>β and P_n =α^n -β^n for each positive integer n, then the value of ((P_17 P_20+5 √ 2 P_17…
If $\displaystyle \alpha, \beta$ are roots of the equation $\displaystyle x^2+5(\sqrt{2}) x+10=0, \alpha>\beta$ and $\displaystyle \mathrm{P}_{\mathrm{n}}=\alpha^{\mathrm{n}}-\beta^{\mathrm{n}}$ for each positive integer n , then the value of $\displaystyle \left(\frac{\mathrm{P}_{17} \mathrm{P}_{20}+5 \sqrt{2} \mathrm{P}_{17} \mathrm{P}_{19}}{\mathrm{P}_{18} \mathrm{P}_{19}+5 \sqrt{2} \mathrm{P}_{18}^2}\right)$ is equal to \_\_\_\_.
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.