If the coefficients of $x^{2}$ and $x^{3}$ in the expansion of ${(3 + ax)}^{9}$ be same, then the value of a is

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3/7

7/3

7/9

9/7

answer is D.

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Detailed Solution

${}^{9}{C_{2}} {(3)}^{7} a^{2} = {}^{9}{C_{3}} {(3)}^{6} a^{3} 3 = \frac{{}^{9}{C_{3}}}{{}^{9}{C_{2}}} (a) 3 = \frac{7}{3} a \Rightarrow a = \frac{9}{7}$

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