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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