If the A.M. between two positive numbers exceeds their G.M. by 2 and the ratio of the numbers
be ` 1: 4 ` find the numbers .

Explanation

Let the number be a and b.
then ` sqrt(ab) + 2 = (a + b)/(2) and (a)/(b) = (1)/(4) rArr b = 4a `
Now , ` sqrt(4a^(2)) = 2 (5a)/(2)`
` rArr 2a + 2 = (5a)/(2)`
`rArr 4a + 2 = 5a`
`rArr a = 4 and b = 16`
Hence number are 4 and 16.