Asked by Kudakwashe
Three numbers in AP have sum 33 and products 1232 .Find the numbers
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Answered by
Kudakwashe
The sum of three numbers in AP is 30 and the sum of their squares is 398 .Find the numbers
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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.
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.
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