If the coefficients of x^2 and x^3 in the expansion of (3 + kx)^9 are equal, then the value of ' k ' is

Step-by-step solution

The general term in the expansion of (3 + kx)^9 is T_ r+1 = ⁹C_ r (3)^ 9-r (kx)^r . For the coefficient of x^2 , we put r = 2 : Coefficient of x^2 = ⁹C₂ (3)⁷ k^2 For the coefficient of x^3 , we put r = 3 : Coefficient of x^3 = ⁹C₃ (3)⁶ k^3 Given that the coefficients are equal: ⁹C₂ (3)⁷ k^2 = ⁹C₃ (3)⁶ k^3 9 8 2 3 = 9 8 7 3 2 k 36 3 = 84 k 108 = 84k k = 108 84 = 9 7 Answer: 9 7