If the coefficient of `x^(2) " and "x^(3)` are equal in the expansion of `(3+ax)^(9)`, then find the value of 'a'

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)`