This is the Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE Board.
Question Number 2 of Exercise 11 B of RS Aggarwal Solution
Here You have to find the Three numbers in AP with the help of their given sum and their product.
Deepak BoraNewbie
Find three numbers in AP whose sum is 15 and product is 80.
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Let a – d, a, a + d are three numbers in AP.
So, their sum = a – d + a + a + d = 15
3a = 15
or a = 5
Again,
Their Product = (a – d) x a x (a + d) = 80
a(a² – d²) = 80
5(5² – d²) = 80
25 – d² = 16
d² = 25 – 16 = 9 = (±3)²
or d = ±3
d = 3 or d = -2
We have 2 conditions here:
At a = 5, d = 3
Numbers are: 2, 5 and 8
At a = 5 and d = -3
Numbers are : 8, 5, 2