Question

In an ap the sum of three numbers is 15and their product is 45. find the three numbers are

Answer 1

Answer:

1, 5, 9

Step-by-step explanation:

let the 3 numbers in AP 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 = 45

(a - d) × a × (a + d) = 45

$(a - d)(a + d) \times 5 = 45 \\ {a}^{2} - {d}^{2} = \frac{45}{5} \\ {5}^{2} - {d}^{2} = 9 \\ 25 - {d}^{2} = 9 \\ - {d}^{2} = 9 - 25 \\ - {d}^{2} = - 16 \\ {d}^{2} = 16 \\ d = \sqrt{16} \\ d = 4$

a = 5 d = 4

the required number are

a - d = 5 - 4 = 1

a = 5

a + d = 5 + 4 = 9

the AP is

1, 5, 9

hope you get your answer

Answer 2

Answer:

the numbers are 1,5, 9 or 9,5,1

$..$

refer to the attachment for the solution.