Let \(\alpha\) and \(\beta\) be the roots of \({x}^{2}+\sqrt{3}x-16=0\), and \(\gamma\) and \(\delta\) be the roots of \…

Let \(\alpha\) and \(\beta\) be the roots of \({x}^{2}+\sqrt{3}x-16=0\), and \(\gamma\) and \(\delta\) be the roots of \({x}^{2}+3x-1=0\). If \({\mathrm{P}}_{\mathrm{n}}={\alpha }^{\mathrm{n}}+{\beta }^{\mathrm{n}}\) and \({\mathrm{Q}}_{\mathrm{n}}={\gamma }^{\mathrm{n}}+{\delta }^{\mathrm{n}}\), 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

[JEE Main 2025, 3 Apr (Shift 1)]