SOLUTION: 1.given that three numbers form an A.P.their sum is 21,and their product is 231.find these numbers.

Algebra ->  Sequences-and-series -> SOLUTION: 1.given that three numbers form an A.P.their sum is 21,and their product is 231.find these numbers.       Log On


   



Question 1006280: 1.given that three numbers form an A.P.their sum is 21,and their product is 231.find these numbers.
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
1. Given that three numbers form an A.P. Their sum is 21,and their product is 231.find these numbers.
-------------------------------------------------------------------

Let  x  be the middle term of this  A.P.
Then the three terms are  (x-d),  x  and  (x+d).

The sum of three is  3x = 21.  Hence,  x = 7.

The product of three is  (7-d)*7*(7+d) = 231,     or
49-d^2 = 231%2F7 = 33.

Hence,  d^2 = 49 - 33 = 16,  and  d = 4.

The three numbers are  7-4 = 3,  7,  and  7+4 = 11.