Find the largest of three numbers in arithmetic progression whose sum is 87 and whose product is 24273Options15192931
Question
Find the largest of three numbers in arithmetic progression whose sum is 87 and whose product is 24273Options15192931
Solution
The three numbers in an arithmetic progression can be represented as (a - d), a, and (a + d), where a is the middle term and d is the common difference.
Given that the sum of the three numbers is 87, we can write the equation:
(a - d) + a + (a + d) = 87 3a = 87 a = 87 / 3 a = 29
The product of the three numbers is given as 24273, so we can write the equation:
(a - d) * a * (a + d) = 24273 (29 - d) * 29 * (29 + d) = 24273 (29^2 - d^2) = 24273 / 29 841 - d^2 = 837 d^2 = 841 - 837 d^2 = 4 d = sqrt(4) d = 2
The largest of the three numbers is (a + d) = 29 + 2 = 31.
So, the largest number is 31.
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