Three numbers in AP have sum 33 and products 1232 .Find the numbers

2 answers

Let the three numbers be a-d, a, and a+d (since they are in AP)
Given that their sum is 33:
(a-d) + a + (a+d) = 33
Simplifying, we get:
3a = 33
a = 11
Now, given that their product is 1232:
(a-d) * a * (a+d) = 1232
Substituting a = 11, we get:
(11-d) * 11 * (11+d) = 1232
121 - d^2 = 112
d^2 = 9
d = 3 or -3
Therefore, the three numbers are either 8, 11, 14 or 14, 11, 8.
The sum of three numbers in AP is 30 and the sum of their squares is 398 .Find the numbers