The ratio of AM and GM of two positive numbers a and b is m:n, show that: a:b=(m+\surd m²-n²):(m-\surd m²-n²

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If the AM and GM of two positive numbers a and b are in the ratio m:n show that
$a : b = (m + \sqrt{m^{2} - n^{2}}) : (m - \sqrt{m^{2} - n^{2}}) .$

Q. The ratio of the A.M and G.M of two positive numbers

a

and

b

, is

m : n

. Show that

a : b = (m + \sqrt{m^{2} - n^{2}}) : (m - \sqrt{m^{2} - n^{2}})

The ratio of the AM and GM of two positive numbers a and b is m : n, show that $a : b = [m + \sqrt{(m^{2} - n^{2})}] : [m - \sqrt{(m^{2} - n^{2})}] .$

Q. The ratio of the A.M and G.M. of two positive numbers a and b , is m : n . Show that .

Q. Given that n numbers of A.Ms are inserted between two sets of numbers

a, 2 b

and

2 a, b

where

a, b \in R .

Suppose further that the

m^{t h}

means between these sets of numbers are same, then the ratio

a : b

equals

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