The sum of three numbers in A.P. is 3 and their product is -35. Find the numbers.
AP GP
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Question

The sum of three numbers in A.P. is 3 and their product is -35. Find the numbers.

KnowledgeBoat · Accepted Answer

Let the three numbers that are in A.P. be a - d, a, a + d. Given, sum of three numbers = 3 ⇒ a - d + a + a + d = 3 ⇒ 3a = 3 ⇒ a = 1. Given, product of the numbers = -35 ⇒ (a - d)(a)(a + d) = -35 Putting the value of a = 1 in the above eq we get, ⇒ (1 - d)(1)(1 + d) = -35 ⇒ (1 - d²) = -35 ⇒ d² = 1 + 35 ⇒ d² = 36 ⇒ d = ⇒ d = +6, -6. ∴ a - d = 1 - 6 = -5 or 1 - (-6) = 7 and a + d = 1 + 6 = 7 or 1 + (-6) = -5 Hence, the numbers are -5, 1, 7.

Mathematics

The sum of three numbers in A.P. is 3 and their product is -35. Find the numbers.

AP GP

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