If the Sum of Three Numbers in A.P., is 24 and Their Product is 440, Find the Numbers. - Mathematics

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If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

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Solution

Let the three numbers in A.P. be a – da, and a + d.

According to the given information,

(a – d) + (a) + (a + d) = 24 … (1)

⇒ 3a = 24

∴ a = 8

(a – da (a + d) = 440 … (2)

⇒ (8 – d) (8) (8 + d) = 440

⇒ (8 – d) (8 + d) = 55

⇒ 64 – d2 = 55

⇒ d2 = 64 – 55 = 9

⇒ = ± 3

Therefore, when d = 3, the numbers are 5, 8, and 11 and when d = –3, the numbers are 11, 8, and 5.

Thus, the three numbers are 5, 8, and 11.

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Chapter 9: Sequences and Series - Miscellaneous Exercise [Page 199]

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NCERT Mathematics Class 11
Chapter 9 Sequences and Series
Miscellaneous Exercise | Q 2 | Page 199

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