# The AM between tw

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

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