Question

Q45.
The sum of three mumbers in AP is 15 and their product is 80. Find the numbers.​

Answer 1

Step-by-step explanation:

let the numbers be a-d, a, a+d

sum of the numbers is 15

a - d + a + a + d = 15

3a = 15

a = 15/3 = 5

product of the numbers is 80

(a - d)(a)(a+d) = 80

(5 - d) × 5 × (5 + d) = 80

(5 - d)(5 + d) = 80/5

5^2 - d^2 = 16

25 - d^2 = 16

- d^2 = 16 - 25

- d^2 = - 9

d^2 = 9

d = √9 = 3

a = 5, d = 3

therefore the numbers are

a - d = 5 - 3 = 2

a = 5

a + d = 5 + 3 = 8

2, 5, 8

verification

sum of the numbers is 15

2 + 5 + 8 = 15

product of the numbers is 80

= 2 × 5 × 8

= 10 × 8

= 80

hope you get your answer