Question

Find the three number in A.P whose sum and product are:
a)6&6
b)15&80
c)15&105
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Answer 1

Let the three number in A.P be (a – d), a and (a + d) respectively.

Given, The three numbers in ap whose sum is 15

So..

(a – d ) + a + (a + d ) = 15

=> 3a = 15

=> a = 5

Again,

The three numbers in ap whose product is 105.

So,

(a – d) a (a + d) = 105

a(a^2 – d^2) = 105

5(25 – d^2) = 105

25 – d^2 = 21

d^2 = 4

d = ± 2

When , d = 2

The three terms of the A.P

= (5 – 2), 5 and (5 + 2)

= 3, 5 and 7

And when, d = – 2

The three terms of the A.P = (5 + 2) 5, and (5 – 2)

= 7, 5 and 3.

So, The numbers are 3,5,7