The AM between two positive numbers a and b(a>b) is twice their GM. Prove that a:b 
.
To prove: Prove that a:b 
Given: Arithmetic mean is twice of Geometric mean.
Formula used: (i) Arithmetic mean between 
(ii) Geometric mean between 
AM = 2(GM)
⇒ a + b = 4
Squaring both side
⇒ (a + b)2 = 16ab … (i)
We know that (a – b)2 = (a + b)2 – 4ab
From eqn. (i)
⇒ (a – b)2 = 16ab – 4ab
⇒ (a – b)2 = 12ab … (ii)
Dividing eqn. (i) and (ii)
⇒ 
Taking square root both side
Applying componendo and dividend
Hence Proved
1