document.write( "Question 621269: Three numbers are in A. P. The difference between the first and the last is 8 and theproduct of these two is 20. Find the numbers. \n" ); document.write( "

Algebra.Com's Answer #390680 by KMST(5328) $\"\"$ $\"About$

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I am assuming that A. P. stands for arithmetic progression (or arithmetic sequence).
\n" ); document.write( "The three numbers are m-d, m, and m+d (m is the middle number and d is the common difference in the arithmetic progression).
\n" ); document.write( "The difference between the first and the last is
\n" ); document.write( " $\"%28m%2Bd%29-%28m-d%29=2d=8\"$ --> $\"highlight%28d=4%29\"$
\n" ); document.write( "The product of the first and the last numbers is
\n" ); document.write( " $\"%28m%2Bd%29%2A%28m-d%29=m%5E2-d%5E2=m%5E2-4%5E2=m%5E2-16=20\"$
\n" ); document.write( " $\"m%5E2-16=20\"$ --> $\"m%5E2=16%2B20\"$ --> $\"m%5E2=36\"$ --> $\"highlight%28m=6%29\"$
\n" ); document.write( "So the numbers would be 6-4, 6, 6+4 or 2, 6, 10.
\n" ); document.write( "But if the numbers are allowed to be negative, we could have $\"highlight%28m=-6%29\"$ and the numbers could be
\n" ); document.write( "-6-4, -6, -6+4 or -10, -6, -2. \n" ); document.write( "

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