If the coefficients of `x^2a n d\ x^3` in the expansion o `(3+a x)^9` are the same, then the value of `a` is `-7/9` b. `-9/7` c. `7/9` d. `9/7`

Answer

N/a

Explanation

`(3+ax)^(9)=overset(9)underset(r=0)(Sigma).^(9)C_(r).(3)^(9-r).(ax)^(r)`
`=^(9)C_(0).3^(9)+^(9)C_(1).3^(8).(ax)^(1)`
`+^(9)C_(2).3^(7)(ax)^(2)+^(9)C_(3).3^(6).(ax)^(3)`
`+…..+^(9)C_(9).(ax)^(9)`
Now , coefficient of `x^(2)`= coefficient of `x^(3)`
`.^(9)C_(2).3^(7).a^(2)=^(9)C_(3).3^(6).a^(3)`
`rArr " "36xx3=84a`
`rArr" "a=(36xx3)/(84)=(9)/(7)`