JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(\alpha\) and \(\beta\) be the roots of \(x^2+\sqrt{3 x}-16=0\), and \(\gamma\) and \(\delta\) be the roots of \(x^2+3 x-1=0\). If \(P_n=\alpha^n+\beta^n\) and \(Q_n=\gamma^n+\delta^n\), then \(\frac{\mathrm{P}_{25}+\sqrt{3 \mathrm{P}_{24}}}{2 \mathrm{P}_{23}}+\frac{\mathrm{Q}_{25}-\mathrm{Q}_{23}}{\mathrm{Q}_{24}}\) is equal to
- A \(3\)
- B \(4\)
- C \(5\)
- D \(7\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & x^2+\sqrt{3} \mathrm{x}-16=0 \lt \beta \\ & \mathrm{P}_{\mathrm{n}}+\sqrt{3} \mathrm{P}_{\mathrm{n}-1}-16 \mathrm{P}_{\mathrm{n}-2}=0 \\ & \mathrm{P}_{25}+\sqrt{3} \mathrm{P}_{24}-16 \mathrm{P}_{23}=0 \\ & \therefore \frac{\mathrm{P}_{25}+\sqrt{3}…
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