This is my doubt:

Find a if the coefficients of x² and x³ in the expansion of (3+ax)⁹are equal.

Thanks a lot. =)

Question

This is my doubt:
Find a if the coefficients of x2 and x3 in
the expansion of (3+ax)9 are equal
Thanks a lot =)

Mayank Bhardwaj · Accepted Answer

rth term in the expansion of (b + x)n is ${}^{n}{C_{r}} b^{n - r} x^{r}$ The coefficient of $u^{r} is {}^{n}{C_{r}} b^{n - r}$ Here b = 3 and x = ax According to the question coefficients of x2 and x3 are equal, then, ${}^{9}{C_{2}} 3^{9 - 2} a^{2} = {}^{9}{C_{3}} 3^{9 - 3} a^{3} \Rightarrow \frac{9!}{2! 7!} \times 3^{7} \times a^{2} = \frac{9!}{3! 6!} \times 3^{6} \times a^{3} \Rightarrow \frac{3 a^{2}}{2 \times 7} = \frac{a^{3}}{3 \times 2} \Rightarrow \frac{9}{7} a^{2} = a^{3} \Rightarrow a^{3} - \frac{9}{7} a^{2} = 0 \Rightarrow a^{2} (a - \frac{9}{7}) = 0 \Rightarrow a - \frac{9}{7} = 0 \Rightarrow a = \frac{9}{7}$

This is my doubt: Find a if the coefficients of x2 and x3 in the expansion of (3+ax)9 are equal. Thanks a lot. =)

This is my doubt:

Find a if the coefficients of x² and x³ in the expansion of (3+ax)⁹are equal.

Thanks a lot. =)