Q. 135.0( 3 Votes )

# If one A.M., A and two geometric means G_{1} and G_{2} inserted between any two positive numbers, show that

Answer :

Let the numbers be a and b.

Now or 2A =a+b

Also, G_{1} and G_{2} are GM between a and b, then a, G_{1}, G_{2}, b are in G.P.

Let r be the common ratio.

Then, b = ar^{4–1} = ar^{3}

⇒

⇒

∴ G_{1} = ar =

G_{2} = ar^{2} =

∴

a + b = 2A

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