The sum of three no of an AP is27 and their product is 405 . Find the

1.	The sum of three no of an AP is27 and their product is 405 . Find the number
Answer» Let the numbers be a - d, a, a + d which are in AP.(a - d) + (a) + (a + d) = 27 .........(1)(a - d)(a)(a + d) = 405 ..........(2)(1) => 3a = 27a = 9(2) => (a2 - d2)(a) = 405[(9)2 - d2] (9) = 405(81 - d2) (9) = 405729 - 9d2 = 4059d2 = 729 - 4059d2 = 324d2 = 36d = 6Now, substitute the values in the 1st equation.(a-d) = 9 - 6 = 3a = 9(a+d) = 9 + 6 = 15Hence the numbers are 3, 9 and 15.

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