Question Detail

The general term: T_{r+1} = C(9,r) 3^{9-r} (ax)^r = C(9,r) 3^{9-r} a^r x^r. Coefficient of x^2 (r=2): C(9,2) 3^{7} a^2 = 36 * 2187 * a^2 = 78732 a^2. Coefficient of x^3 (r=3): C(9,3) 3^{6} a^3 = 84 * 729 * a^3 = 61236 a^3. Set them equal: 78732 a^2 = 61236 a^3 => divide by a^2 (a≠0): 78732 = 61236 a => a = 78732/61236 = simplify dividing by 12: 6561/5103 = divide by 3: 2187/1701 = divide by 3: 729/567 = divide by 9: 81/63 = divide by 9: 9/7. So a = 9/7. The options are negative, so perhaps the expansion is (3 - ax)^9 or the coefficients are same in magnitude but opposite sign? If they are the same value, a = 9/7. Since options are negative, maybe a = -9/7 would make one coefficient negative if the sign is considered. Given the options, A is -9/7.