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 " "36xx 3= 84 a`
`rArr " "a=(36xx3)/(84) =(9)/(7)`