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

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Question 1187157: The coefficient of x^2 is 69 in the expansion of (1-ax)^24, where a > 0. Find the coefficient of x^3.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


In the expansion of %281-ax%29%5E24, the coefficient of the x^2 term is

C%2824%2C2%29%281%5E22%29%28%28-a%29%5E2%29

Given that that coefficient is 69, we have

%28%2824%2A23%29%2F2%29%281%29%28x%5E2%29=69
12x%5E2=3
x%5E2=1%2F4
x+=+1%2F2 OR x+=+-1%2F2

So there are going to be two different possible answers for the coefficient of x^3.

ANSWER #1: C%2824%2C3%29%281%5E21%29%28%281%2F2%29%5E3%29=253

ANSWER #2: C%2824%2C3%29%281%5E21%29%28%28-%281%2F2%29%29%5E3%29=-253