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, T_r+1 of binomial expansionis given by,

T_r+1 ⁿC_r x^n-r y^r where

ⁿC_r

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

T_r+1 ⁹C_r

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