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

 ncert cbse chapter 8 binomial theorem miscellaneous exercise

2

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

 

using binomial theorem

{(3+ax)^9}= 3^9 + C(9,1)(3^8){(ax)}+ C(9,2)(3^7){(ax)^2} 

        + C(9,3)(3^6){(ax)^3} + ...+{(ax)^9}

 

given coefficients of (x^2)  & (x^3) are equal

therfore

 C(9,2)(3^7){(a)^2} =C(9,3)(3^6){(a)^3}

36* (3^7){(a)^2}=84*(3^6){(a)^3}

if a cannot be zero 

a= {36*(3^7) }/{84*(3^6)}

a =9/7

chapter 8 binomial theorem miscellaneous exercise

 1.Find a , b and n in the expansion of (a+b)^n if the first three terms in the expansion are 729, 7290, 30375

solution

 

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

solution

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