Let αn and βn are positive integers, such that 2αn+3βn=3+22n, 2αn2-3βn2=1 and limn→∞αnβn=p, then 4p2 is

Question

Let

α_{n}

and

β_{n}

are positive integers, such that

\sqrt{2} α_{n} + \sqrt{3} β_{n} = {(3 + 2 \sqrt{2})}^{n}, 2 {(α_{n})}^{2} - 3 {(β_{n})}^{2} = 1

and

\lim_{n \to \infty} \frac{α_{n}}{β_{n}} = \sqrt{p}

, then

4 p^{2}

Correct Answer

Please login to view the detailed solution steps...