Q13 of 176 Page 21

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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