#### Question :

If one AM ‘a’ and two GM’s p and q are inserted between any two given numbers then find value of 2A Submitted on 10/7/2024 | Answered by Vandana Rana#### Answer :

Let the numbers be x and yA is their A . M .

2 A = x + y....... (1)

Also p , q are two geometric means between x and y

∴ x , p , q , y are in G . P .

Since x , p , q are in G . P .

∴ p

^{2}= x q

or x= p

^{2}/q.......(2)

Since p , q , y are in G . P .

∴ q

^{2}= p y

y= q

^{2}/p..... ....(3)

Adding (2)and (3)

x+y =p

^{2}/q +q

^{2}/p

x+y =( p

^{3}+q

^{3})/pq

put it in (1)

2A =(p

^{3}+q

^{3})/pq