If the fourth term in the expansion of `(a x+1/x)i s5/2,\ ` then find the values of `a\ a n d\ ndot`

Options

A. `(1)/(2),6`
B. 1,3
C. `(1)/(2),3`
D. cannot be found

Answer

A

Explanation

It is given that the fouth term in the expansion of
`(ax+ (1)/(x))^(n) is (5)/(2)`
`therefore ""^(n)C_(3) (a x)^(n-3) ((1)/(x))(3) = (5)/(2)`
`rArr ""^(n)C_(3)a^(n-2) x^(n-6) = (5)/(2)` ….(i)
`rArr n-6 = 0 [because ` RHS is independent of x]
Putting n=6 in (i) , we get
`""^(6)C_(3) a^(3) = (5)/(2) rArr a^(3) = (1)/(8) rArr a = (1)/(2)`
Hence , n = 6 a ` = (1)/(2)` .