document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #818111 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "In the expansion of $\"%281-ax%29%5E24\"$ , the coefficient of the x^2 term is

\n" ); document.write( " $\"C%2824%2C2%29%281%5E22%29%28%28-a%29%5E2%29\"$

\n" ); document.write( "Given that that coefficient is 69, we have

\n" ); document.write( " $\"%28%2824%2A23%29%2F2%29%281%29%28x%5E2%29=69\"$
\n" ); document.write( " $\"12x%5E2=3\"$
\n" ); document.write( " $\"x%5E2=1%2F4\"$
\n" ); document.write( " $\"x+=+1%2F2\"$ OR $\"x+=+-1%2F2\"$

\n" ); document.write( "So there are going to be two different possible answers for the coefficient of x^3.

\n" ); document.write( "ANSWER #1: $\"C%2824%2C3%29%281%5E21%29%28%281%2F2%29%5E3%29=253\"$

\n" ); document.write( "ANSWER #2: $\"C%2824%2C3%29%281%5E21%29%28%28-%281%2F2%29%29%5E3%29=-253\"$
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