The sum of three consecutive terms in A.P. is 24 product is 440, find the terms.

Q. The sum of three consecutive terms in A.P. is 24 product is 440, find the terms.
Solution:
Let us assume that the numbers are a-d, a, a+d
Given,
(a-d)+a+(a+d)=24
⇒3a=24
⇒a=24/3
⇒a=8

and (a-d)*a*(a+d)=440
⇒(8-d)*8*(8+d)=440
⇒(8-d)(8+d)=440/8
⇒8²-d²=55   (since (a+b)(a-b)=a²-b²)
⇒64-d²=55
⇒-d²=55-64
⇒-d²=-9
⇒d²=9
⇒d²=3²
⇒d=±3

If d=3, then the numbers are 8-3,8,8+3 => 5,8,11
If d=-3, then the numbers are 8-(-3), 8, 8+(-3)=>8+3, 8, 8-3 =>11, 8, 5