x^2 - √2x - √3 = 0 and P_n = α^n + β^n. The value of P(12) - √2P_{11} - √3P_{10} + P_{11} - √2P_10 is

Question

\(x^2 - 2\sqrt x - \sqrt 3 = 0\) and \(P_n =\alpha^n + \beta ^n\). The value of \(P_{12 } - \sqrt 2P_{11} - \sqrt 3 P_{10} + P_{11} - \sqrt 2P_{10}\) is

(1) \(\sqrt 3 P_9\)

(2) \((2 + \sqrt 5) P_9\)

(3) \(\sqrt 5 P_9\)

(4) \((3 + \sqrt 5) P_9\)

Answer 1

Correct option is (1) \(\sqrt 3 P_9\)