Let `alpha` and `beta` are roots of `x^(2) - 17x - 6 = 0` with `alpha gt beta, if a_(n) = alpha^(n+2)+beta^(n+2)` for `n ge 5` then the value of `(a_(10)-6a_(8)-a_(9))/(a_(9))`

Options

A. `6`
B. `16`
C. `12`
D. `8`

Answer

B

Explanation

Let `alpha` and `beta` ………..
Let `alpha` and `beta` asre roots of `x^(2)-17x-6=0`
`alpha^(2)-17alpha-6=0`
`alpha^(n+2)-17alpha^(n+1)-6alpha^(n)=0`
`beta^(n+2)-17beta^(n+1)-6beta^(n)=0`
By (1) and (2)
`a_(n)-17a_(n-1)-6a_(n-2)=0`
`a_(10)-17a_(9)-6a_(8) = 0`
`a_(10)-6a_(8)-a_(9)=16a_(9)`
`implies (a_(10)-6a_(8)-a_(9))/(a_(9)) = 16`