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