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 \( P_n=\alpha^n+\beta^n \) and \( Q_n=\gamma^n+\delta^n \), then \( \dfrac{P_{25}+\sqrt{3}P_{24}}{2P_{23}}+\dfrac{Q_{25}-Q_{23}}{Q_{24}} \) is equal to:
