Question

If the coefficients of X^2 and X^3 in the expansion of (3+kx)^9 are equal, find the value of k.

Answer 1

the two terms are

C(9,2) 3^7 (kx)^2, C(9,3) 3^6 (kx)^3
so the coefficients are
78732 k^2, 61236 k^3
since
78732 = 8748*9
61236 = 8748*7
9k^2 = 7k^3
k = 9/7