Let α and β be the roots of the equation, 5 x 2 + 6 x - 2 = 0 . If S n = α n + β n ,   n = 1 ,   2 ,   3 ,   . . . . , then

Question

Let &#945; and &#946; be the roots of the equation, 5 x 2 + 6 x - 2 = 0 . If S n = &#945; n + &#946; n , &#160; n = 1 , &#160; 2 , &#160; 3 , &#160; . . . . , then

Aicharya · Accepted Answer

If &#945; , &#160; &#946; are roots of quadratic equation 5 x 2 + 6 x - 2 = 0 &#8658; &#160; 5 &#945; 2 + 6 &#945; - 2 = 0 &#160; &#8658; 5 &#945; 2 + 6 &#945; = 2 &#8658; &#160; 5 &#946; 2 + 6 &#946; - 2 = 0 &#160; &#8658; 5 &#946; 2 + 6 &#946; = 2 5 S 6 + 6 S 5 = 5 &#945; 6 + &#946; 6 + 6 &#945; 5 + &#946; 5 = &#945; 4 5 &#945; 2 + 6 &#945; + &#946; 4 5 &#946; 2 + 6 &#946; = 2 &#945; 4 + &#946; 4 = 2 S 4

Let α and β be the roots of the equation, 5 x 2 + 6 x - 2 = 0 . If S n = α n + β n ,…

Solution

Let &#945; and &#946; be the roots of the equation, 5 x 2 + 6 x - 2 = 0 . If S n = &#945; n + &#946; n ,…

Solution

Let α and β be the roots of the equation, 5 x 2 + 6 x - 2 = 0 . If S n = α n + β n ,…