Find a if the coefficients of x^{2} and x^{3} | vedclass

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(A) The general term in the expansion of $(x+y)^{n}$ is given by $T_{r+1} = {}^{n}C_{r} x^{n-r} y^{r}$.For the expansion of $(3+ax)^{9}$,the general t

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$9/7$

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(A) The general term in the expansion of $(x+y)^{n}$ is given by $T_{r+1} = {}^{n}C_{r} x^{n-r} y^{r}$.For the expansion of $(3+ax)^{9}$,the general term is $T_{r+1} = {}^{9}C_{r} (3)^{9-r} (ax)^{r} = {}^{9}C_{r} (3)^{9-r} a^{r} x^{r}$.To find the coefficient of $x^{2}$,we set $r=2$:Coefficient of $x^{2} = {}^{9}C_{2} (3)^{9-2} a^{2} = \frac{9 	imes 8}{2 	imes 1} (3)^{7} a^{2} = 36 	imes 3^{7} a^{2}$.To find the coefficient of $x^{3}$,we set $r=3$:Coefficient of $x^{3} = {}^{9}C_{3} (3)^{9-3} a^{3} = \frac{9 	imes 8 	imes 7}{3 	imes 2 	imes 1} (3)^{6} a^{3} = 84 	imes 3^{6} a^{3}$.Given that the coefficients are equal:$84 	imes 3^{6} a^{3} = 36 	imes 3^{7} a^{2}$.Dividing both sides by $12 	imes 3^{6} a^{2}$ (assuming $a 
eq 0$):$7a = 3 	imes 3 = 9$.Therefore,$a = 9/7$.

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

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