One of the basic question from arithmetic progression chapter in which we are find three numbers in AP is their sum is 15 and product is 80.
RS Aggarwal, Class 10, chapter 5B, question no 6.
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let a−d,a,a+d are three terms of an AP
according to the problem given,
sum of the terms=15
a−d+a+a+d=15
3a=15
a=15/3
a=5
product=80
(a−d)a(a+d)=80
(a²−d²)a=80
(5²−d²)5=80
25−d²=80/5
25−d²=16
−d²=−9
d²=3²
d=±3
Therefore,a=5,d=±3
required 3terms are
a−d=5−3=2
a=5
a+d=5+3=8
(2,5,8)or(8,5,2)