SOLUTION: THREE NUMBERS IN ARITHMETIC PROGRESSION HAVE THE SUM OF 33 AND PRODUCT OF 1232. FIND THE THREE NUMBERS.

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Question 421258: THREE NUMBERS IN ARITHMETIC PROGRESSION HAVE THE SUM OF 33 AND PRODUCT OF 1232. FIND THE THREE NUMBERS.
Answer by dnanos(83) About Me  (Show Source):
You can put this solution on YOUR website!
Let x-d, x, x+d the unknown numbers.
(x-d)+x+(x+d)=x+x+x=3x
3x=33
x=33/3
x=11
Now we have to find "d":
%2811-d%29%2A11%2A%2811%2Bd%29=1232
11%2811%5E2-d%5E2%29=1232
11%2A121-11d%5E2=1232%7D%7D%0D%0A%7B%7B%7B1331-11d%5E2=1232
-11d%5E2=1232-1331
-11d%5E2=-99
d%5E2=%28-99%29%2F%28-11%29%7D%7D%0D%0A%7B%7B%7Bd%5E2=9
d=%2Bsqrt%289%29or d=-sqrt%289%29
d=3 or d=-3
(i)for d=3
x-d=8 x=11 x+d=14
(ii)For d=-3
x-d=14 x=11 x+d=8
So the numbers are 8,11 and 14.