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

Question

Philoid · Accepted Answer

We know that-

General term of expansion (a+b)ⁿ is

For (3+ax)⁹

Putting a = 3, b = ax & n = 9

General term of (3+ax)⁹ is

Since we need to find the coefficients of x² and x³, therefore

For r = 2

Thus, the coefficient of x² =

For r = 3

Thus, the coefficient of x³ =

Given that-

Coefficient of x² = Coefficient of x³

∴ a = 9/7

Hence, a = 9/7