If two geometric means g1 and g2 and one arithmetic  mean A be inserted between two numbers, then g12g2+g22g1=

Let the two numbers be a and b.∴ A=a+b2 or 2A=a+b     (1)Again, a, g1, g2, b are in G.P.∴ g1a=g2g1=bg2Now, g1a≡g2g1⇒g12g2≡aand g2g1=bg2⇒g22g1=b∴ a+b=g12g2+g22g1           (2)∴  From Eqs (1) and (2), we get  2A=g12g2+g22g1