Let α and β be two real numbers such that α + β = 1 and α β = - 1 . Let p n = α n + β n , p n - 1 = 11 and p n + 1 = 29 for some integer n ⩾ 1 . Then, the value of p n 2 is______.

Question

Let &#945; and &#946; be two real numbers such that &#945; + &#946; = 1 and &#945; &#946; = - 1 . Let p n = &#945; n + &#946; n , p n - 1 = 11 and p n + 1 = 29 for some integer n &#10878; 1 . Then, the value of p n 2 is______.

Aicharya · Accepted Answer

x 2 - x - 1 = 0 roots = &#945; , &#946; &#945; 2 - &#945; - 1 = 0 &#8658; &#945; n + 1 = &#945; n + &#945; n - 1 &#946; 2 - &#946; - 1 = 0 &#8658; &#946; n + 1 = &#946; n + &#946; n - 1 &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; + &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; p n + 1 = p n + p n - 1 29 = p n + 11 p n = 18 p n 2 = 324

Let α and β be two real numbers such that α + β = 1 and α β = - 1 . Let p n =…

Solution

Let &#945; and &#946; be two real numbers such that &#945; + &#946; = 1 and &#945; &#946; = - 1 . Let p n =…

Solution

Let α and β be two real numbers such that α + β = 1 and α β = - 1 . Let p n =…