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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))`A. `6`B. `16`C. `12`D. `8` |
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Answer» Correct Answer - B 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` |
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