Q. 135.0( 3 Votes )
If one A.M., A and two geometric means G1 and G2 inserted between any two positive numbers, show that 
Answer :
Let the numbers be a and b.
Now 
or 2A =a+b
Also, G1 and G2 are GM between a and b, then a, G1, G2, b are in G.P.
Let r be the common ratio.
Then, b = ar4–1 = ar3
⇒ 
⇒ 
∴ G1 = ar = 
G2 = ar2 = 
∴ 
a + b = 2A
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