2. The sum of three numbers in A.P. is 27 and their product is 405. Find the numbers.
Question
The sum of three numbers in A.P. is 27 and their product is 405. Find the numbers.
Solution
Sure, let's solve this step by step.
Given that the sum of three numbers in A.P. is 27 and their product is 405.
Let's denote the three numbers as a-d, a, a+d. They are in A.P. and their sum is 27.
So, we have the equation:
(a-d) + a + (a+d) = 27 3a = 27 a = 27/3 a = 9
The product of the three numbers is 405, so we have the equation:
(a-d)a(a+d) = 405 (9-d)9(9+d) = 405 (81-d^2) = 405/9 81-d^2 = 45 d^2 = 81-45 d^2 = 36 d = sqrt(36) d = 6 or d = -6
So, the three numbers are 9-6=3, 9, 9+6=15 or 9+6=15, 9, 9-6=3.
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