Question

The coefficient of x^2 is 69 in the expansion of (1-ax)^24, where a>0. Find the coefficient of x^3.

Answer 1

(1-ax)^24
= 1 + C(24,1)(-ax) + C(24,2)(-ax)^2 + ...

so C(24,2)(a^2)x^2 = 69x^2
276a^2 = 69
a^2 = 69/276 = 1/4
a = ±1/2

if a = 1/2
term containing x^3 = C(24,3)(-x/2)^3
= -2024/8x^3 = -253x^3

if a = -1/2
term containing x^3 = C(24,3(x/2)^3 = 253x^3

Answer 2

thanks