If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are 
.
It is given that A and G are A.M. and G.M. between two positive numbers. Let these two positive numbers be a and b.
∴ 
From (1) and (2), we obtain
a + b = 2A … (3)
ab = G2 … (4)
Substituting the value of a and b from (3) and (4) in the identity (a – b)2 = (a + b)2 – 4ab, we obtain
(a – b)2 = 4A2 – 4G2 = 4 (A2–G2)
(a – b)2 = 4 (A + G) (A – G)
From (3) and (5), we obtain
Substituting the value of a in (3), we obtain
Thus, the two numbers are 
.
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thank u very much sir or madam
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