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
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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