If the coefficients of x^2 and x^3 in the expansion of (3 + px)^9 are the same then prove that P = 9/7. ​

Question

If the coefficients of x² and x³ in the expansion of (3 + px)⁹ are the same then prove that P = \(\frac{9}7\).

Answer 1

To prove: that. If the coefficients of x² and x³ in the expansion of (3 + px)⁹ are the same then P = \(\frac{9}7\)

Formula Used: 

General term, T_r+1 of binomial expansion (x + y)ⁿ is given by,

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

For finding the term which has x² in it, is given by

 r = 2 

Thus, the coefficients of x² are given by,

For finding the term which has x² in it, is given by 

r = 3 

Thus, the coefficients of x³ are given by,

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

Thus, the value of p for which coefficients of x² and x³ in the expansion of (3 + px)⁹ are the same is = \(\frac{9}7\)