Question

The sum of three positive integers in AP is 24 and their product is 480 find the numbers

Answer 1

Let the three terms in AP be  a-d , a , a+d

Now we are given that The sum of three numbers in A.P is 24

So,

A+d+a+a-d=24

A=8

We are also given that their product is 480

( a+d) a (a-d) =480

(a³-ad²) =480

Substitute the value of d from 1

(8³-8d²) =480

d=-2, 2

At a = 8 and d = -2

a+d=8-2=6

a=8

a-d=8+2=10

At a = 8 and d = 2

a+d=8+2=10

a=8

a-d=8-2=6