Question:
if the sum of three numbers in an A.P is 24 and their product is 440 . find their sum
Answer:
Let the three numbers in AP are: a - d, a, a + d
Given sum of the numbers = 24
=> a - d + a + a + d = 24
=> 3a = 24
=> a = 24/3
=> a = 8
Again, given product of the numbers = 440
=> (a - d)*a*(a + d) = 440
=> (8 - d)*8*(8 + d) = 440
=> (8 - d)*(8 + d) = 440/8
=> (8 - d)*(8 + d) = 55
=> 82 - d2 = 55
=> 64 - d2 = 55
=> d2 = 64 - 55
=> d2 = 9
=> d = ±√9
=> d = ±3
Now, when a = 8 and d = 3, the numbers are
8 - 3, 8, 8 + 3 = 5, 8, 11
So, sum = 5 + 8 + 11 = 24
Now, when a = 8 and d = -3, the numbers are
8 + 3, 8, 8 - 3 = 11, 8, 5
So, sum = 11 + 8 + 5 = 24
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