Let the sum of three numbers in A.P is 24 and their product is 440. Find the numbers

Solution:

Let the three numbers in A.P be (a - d), a and (a + d)

According to the given information,

(a - d ) + (a) + (a - d ) = 24

⇒ 3a = 24

⇒ a = 8 ....(1)

And,

(a - d) (a) (a - d) = 440

⇒ (8 - d)(8)(8 + d) = 440 [from (1)]

⇒ (8 - d) (8 + d) = 55

⇒ 64 - d² = 55

⇒ d² = 9

⇒ d = ± 3

Therefore,

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

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

Thus, the three numbers are 5,8 and 11

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NCERT Solutions Class 11 Maths Chapter 9 Exercise ME Question 2

Let the sum of three numbers in A.P is 24 and their product is 440. Find the numbers

Summary:

It is known that the sum of three numbers in A.P is 24 and their product is 440. The numbers are 5,8 and 11