Let α and β be the roots of x 2 - 6 x - 2 = 0 . If a n = α n - β n for n ⩾ 1 , then the value of a 10 - 2 a 8 3 a 9 is:

Question

Let &#945; and &#946; be the roots of x 2 - 6 x - 2 = 0 . If a n = &#945; n - &#946; n for n &#10878; 1 , then the value of a 10 - 2 a 8 3 a 9 is:

Aicharya · Accepted Answer

&#945; 2 - 6 &#945; - 2 = 0 &#945; 10 - 6 &#945; 9 - 2 &#945; 8 = 0 &#946; 10 - 6 &#946; 9 - 2 &#946; 8 = 0 &#945; 10 - &#946; 10 - 6 &#945; 9 - &#946; 9 - 2 &#945; 8 - &#946; 8 = 0 &#8658; a 10 - 6 a 9 - 2 a 8 = 0 &#8658; a 10 - 2 a 8 3 a 9 = 2

Let α and β be the roots of x 2 - 6 x - 2 = 0 . If a n = α n - β n for n ⩾ 1 ,…

Solution

Let &#945; and &#946; be the roots of x 2 - 6 x - 2 = 0 . If a n = &#945; n - &#946; n for n &#10878; 1 ,…

Solution

Let α and β be the roots of x 2 - 6 x - 2 = 0 . If a n = α n - β n for n ⩾ 1 ,…