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 {P_{25}+\sqrt{3} P_{24}}/{2 P_{23}}+ {Q_{25}-Q_{23}}/{Q_{24}} is equal to [3 Apr 2025 Shift 1]

JEE Main 3 Apr 2025 Shift 1 Paper

Section: Mathematics

Question : 18 of 75

Marks: +1, -0

Let α and β be the roots of x2+√3x−16=0, and γ and δ be the roots of x2+3x−1=0. If Pn=αn+βn and Qn=γn+δn, then ‌

P25+√3P24

2P23

+‌

Q25−Q23

Q24

is equal to

[3 Apr 2025 Shift 1]

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