SOLUTION: 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.

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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.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I am assuming that A. P. stands for arithmetic progression (or arithmetic sequence).
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).
The difference between the first and the last is
%28m%2Bd%29-%28m-d%29=2d=8 --> highlight%28d=4%29
The product of the first and the last numbers is
%28m%2Bd%29%2A%28m-d%29=m%5E2-d%5E2=m%5E2-4%5E2=m%5E2-16=20
m%5E2-16=20 --> m%5E2=16%2B20 --> m%5E2=36 --> highlight%28m=6%29
So the numbers would be 6-4, 6, 6+4 or 2, 6, 10.
But if the numbers are allowed to be negative, we could have highlight%28m=-6%29 and the numbers could be
-6-4, -6, -6+4 or -10, -6, -2.