Q. 134.2( 4 Votes )

If A is the arith

Answer :

Let the two numbers be ‘a’ and ‘b’


The arithmetic mean is given by and the geometric mean is given by


We have to insert two geometric means between a and b


Now that we have the terms a, G1, G2, b


G1 will be the geometric mean of a and G2 and G2 will be the geometric mean of G1 and b


Hence and


Square


G12 = aG2


Put



Square both sides


G14 = a2(G1b)


G13 = a2b



Put value of G1 in






Now we have to prove that


Consider RHS



Substitute values of G1 and G2 from (i) and (ii)





RHS = a + b


Divide and multiply by 2



But


Hence


RHS = 2A


Hence RHS = LHS


Hence proved


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