Q. 24.6( 26 Votes )

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

Answer :

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

According to question -

(a – d) + (a) + (a + d) = 24 … (1)

⇒ 3a = 24

∴ a = 8

and,

also product of these numbers is 440,(a – d) a (a + d) = 440 … (2)

⇒ (8 – d) (8) (8 + d) = 440

⇒ (8 – d) (8 + d) = 55

⇒ 64 – d^{2} = 55

⇒ d^{2} = 64 – 55 = 9

⇒ d = 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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RD Sharma - Mathematics