1.If α,β\alpha, \betaα,β are roots of the equation x2+52 x+10=0x^2 + 5\sqrt{2}\,x + 10 = 0x2+52x+10=0, α>β\alpha > \betaα>β and Pn=αn−βnP_n = \alpha^n - \beta^nPn=αn−βn for each positive integer nnn, then the value ofP17 P20+52 P17 P19P18 P19+52 P17 P18\dfrac{P_{17}\,P_{20} + 5\sqrt{2}\,P_{17}\,P_{19}}{P_{18}\,P_{19} + 5\sqrt{2}\,P_{17}\,P_{18}}P18P19+52P17P18P17P20+52P17P19is equal to:a.2+12−1\dfrac{\sqrt{2} + 1}{\sqrt{2} - 1}2−12+1b.2−12+1\dfrac{\sqrt{2} - 1}{\sqrt{2} + 1}2+12−1c.2+12+2\dfrac{\sqrt{2} + 1}{\sqrt{2} + 2}2+22+1d.2\sqrt{2}2Login to continueOnly logged in users canattempt or see the solution.
