The coefficient of $x^2$ and $x^3$ in the expansion of $(3+a x)^9$ are equal, then $\mathrm{a}=$

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Professor PC Thomas Classes · Answer

Coefficient of $x^2$ is ${ }^9C_2 3^7 a^2$. Coefficient of $x^3$ is ${ }^9C_3 3^6 a^3$. Equating: $36 \cdot 3^7 a^2 = 84 \cdot 3^6 a^3 \implies \frac{36 \cdot 3}{84} = a \implies a = \frac{108}{84} = \frac{9}{7}$.