Question:
If the coefficients of x2 and x3 in the expansion of (3 + ax)9 are the same, then the value of a is
(a) $-\frac{7}{9}$
(b) $-\frac{9}{7}$
(c) $\frac{7}{9}$
(d) $\frac{9}{7}$
Solution:
(d) $\frac{9}{7}$
Coefficients of x2 = Coefficients of x3
${ }^{9} C_{2} \times 3^{9-2} a^{2}={ }^{9} C_{3} \times 3^{9-3} a^{3}$
$\Rightarrow a=\frac{{ }^{9} C_{2}}{{ }^{9} C_{3}} \times 3$
$=\frac{9 ! \times 3 ! \times 6 ! \times 3}{2 ! \times 7 ! \times 9 !}$
$=\frac{9}{7}$
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