Question

Find $a$ if the coefficients of $x^2$ and $x^3$ in the expansion of $(3+ax{)}^9$ are equal.

Answer 1

Coefficient of $x^2$ is given by ${}^9{C}_2{3}^7{a}^2$ and coefficient of $x^3$ is given by ${}^9{C}_3{3}^6{a}^3$

Equating both the coefficients, we get

${}^9{C}_2{3}^7{a}^2={}^9{C}_3{3}^6{a}^3$

$\Rightarrow a=\frac{9}{7}$