If one A.M., A and two geometric means G1 and G2 inserted between any two positive numbers,show that G1 2 / G2 + G22 / G1 = 2A.

Let b and c be two positive numbers. Then,

A = A.M. of b and c

Again, G1 and G2 be two geometric means between b and c. Then, b, G1, G2 , c are in G.P. with common ratio

Therefore,  G1 = br  and G2 = br2  

Now,

[Hence proved]

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