If the quadratic equation `x^(2)-36x+lambda=0` has roots `alpha` and `beta` such that `alpha`, `beta in N` and `(lambda)/(5) cancel in Z` and `lambda` assumes minimum possible value then `(sqrt(alpha+2)sqrt(beta+2))/(|alpha-beta|)` is equal to (a) `(3)/(8)` (b) `(3)/(16)` (c) `(sqrt(111))/(34)` (d) `(sqrt(111))/(17)`

Options

A. `(3)/(8)`
B. `(3)/(16)`
C. `(sqrt(111))/(34)`
D. `(sqrt(111))/(17)`

Answer

A

Explanation

`(a)` `x^(2)-36x+lambda=0`
`:. Lambda=36x-x^(2)`
`alpha=1`, `lambda=5`, `beta=35` (rejected)

`:.alpha=2`, `lambda=68`, `beta=34` or `alpha=34`, `beta=2`
`:. (sqrt(36)sqrt(4))/(32)=(3)/(8)`