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 RanaAnswer :
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 .
∴ p2 = x q
or x= p2/q.......(2)
Since p , q , y are in G . P .
∴ q2 = p y
y= q2/p..... ....(3)
Adding (2)and (3)
x+y =p2/q +q2/p
x+y =( p3 +q3)/pq
put it in (1)
2A =(p3 +q3)/pq