Roots of Quadratic Equations (Jee Mains)

Advanced Series

Hard

Roots of Quadratic Equations

Let α and β be the roots of ${x^2} + \sqrt {3x} - 16 = 0$ , and γ and δ be the roots of x² + 3x –1 = 0. If P_n = αⁿ + βⁿ and ${Q_n} = {\gamma ^n} + {\delta ^n}$ , then $\frac{{{P_{25}} + \sqrt {3{P_{24}}} }}{{2{P_{23}}}} + \frac{{{Q_{25}} - {Q_{23}}}}{{{Q_{24}}}}$ is equal to

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