Question

The sum of three numbers in A.P. is 24 and their product is 440. Find the numbers.
Please answer fast

Answer 1

Hii There!!

Here is your answer..


Let the three numbers in A.P. be a – d, a, and a + d.
According to the question :-

(a – d) + (a) + (a + d) = 24 ----- (1)

=) 3a = 24

=) a = 8

(a – d) a (a + d) = 440 ---- (2)

=) (8 – d) (8) (8 + d) = 440

=) (8 – d) (8 + d) = 55

=) 64 – d2 = 55

=)  d2 = 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.

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


Hope it helps

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Answer 2

Answer:

A.P. means arithmetic progression. It means the series which the common difference between any two consecutive terms is equal.

Sum of three numbers = 24

product = 440

Explanation:

Let the three numbers be a1, a2, a3

a1 = a

a2 = a+d

a3= a+2d

the sum is 24

a + a + d + a + 2d = 24

3a + 3d = 24

3(a+d)= 24

a+d= 8

a= 8-d

their product is 440

(a)(a+d)(a+2d) = 440

(8-d)(8-d+d)(8-d+2d)= 440

(8-d)(8)(8+d)=440

(a+b)(a-b)= a^2-b^2

$64 - {d}^{2} (8) = 440 \\ 64 - {d}^{2} = 55 \\ 64 - 55 = {d}^{2}$

$9 = {d}^{2} \\ d = 3$

a= 8-d

a=8-3=5

a1=5

a2= a+d=5+3=8

a3= a+2d= 5+2(3) = 11

the numbers are 5,8 and 11.