Question

Find three number in ap whose sum is 15 and the product is80

Answer 1

2,5,8 are three numbers which are in ap

Answer 2

Answer:

(2,5,8), (8,5,2)

Step-by-step explanation:

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

We are given that sum of these three numbers is 15 and the product of these numbers is 80, therefore

(a-d)+(a)+(a+d)=15

⇒3a=15

⇒a=5

Also, $(a-d)(a)(a+d)=80$

⇒$(a^{2}-d^{2})(a)=80$

⇒$a^{3}-ad^{2} =80$

Putting a=5, we have

⇒$125-5d^{2}=80$

⇒$45=5d^{2}$

⇒$d$=±$3$

If d=3, then a-d=2, a+d=8, then the three numbers will be:2,5,8

If d=-3, then a-d=8, a+d=2, then the number will be: 8,5,2