Answer :

To prove: that. If the coefficients of x2 and x3 in the expansion of (3 + px)9 are the same then .


Formula Used:


General term, Tr+1 of binomial expansionis given by,


Tr+1 nCr xn-r yr where


nCr


Now, finding the general term of the expression, (3 + px)9 , we get


Tr+1 9Cr


For finding the term which has in it, is given by


r=2


Thus, the coefficients of x2 are given by,


T3 9C2


T3 9C2


For finding the term which has in it, is given by


r=3


Thus, the coefficients of x3 are given by,


T3 9C3


T3 9C3


As the coefficients of x2 and x3 in the expansion of (3 + px)9 are the same.


9C3 9C2


9C3 9C2





Thus, the value of p for which coefficients of x2 and x3 in the expansion of (3 + px)9 are the same is


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