Question

if one gm H and twi Am s p and q are inserted between two given position numbers prove that G^2=(2p-q)(2q-p)​

Answer 1

Answer:

Let the two numbers be a and b, then

G=

ab

⇒G

2

=ab

Also, p and q are two A.M.'s between a and b

∴a,p,q,b are in A.P.

∴p−a=q−p and q−p=b−q

∴a=2p−q and b=2q−p

∴G

2

=ab=(2p−q)(2q−p)