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


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