If the A.M. of two positive numbers `aa n db(a > b)` is twice their geometric mean. Prove that : `a : b=(2+sqrt(3)):(2-sqrt(3))dot`

If the arithmetic means of two positive number a and b (a gt b ) is twice their geometric mean, then find the ratio a: b

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 sum of two numbers is 6 times their geometric means, show that numbers are in the ratio (3+2sqrt(2)):(3-2sqrt(2)) .

The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio (3+2sqrt2):(3-2sqrt2) .

The sum of two numbers is 6 times their geometric mean, show that the numbers are in the ratio (3 + 2sqrt(2)) : (3 - 2sqrt(2))

The arithmetic mean between a and b is twice the geometric mean between a and b. Prove that : (a)/(b) = 7+ 4sqrt3 or 7- 4sqrt3

If the A.M. of two numbers is twice their G.M., show that the numbers are in the ratio (2+sqrt(3)):(2-sqrt(3)).

The arithmetic mean of two positive numbers a and b exceeds their geometric mean by 2 and the harmonic mean is one - fifth of the greater of a and b, such that alpha=a+b and beta=|a-b| , then the value of alpha+beta^(2) is equal to

The arithmetic mean of two positive numbers a and b exceeds their geometric mean by (3)/(2) and the geometric mean exceeds their harmonic mean by (6)/(5) . If a+b=alpha and |a-b|=beta, then the value of (10beta)/(alpha) is equal to

If A.M. and G.M. between two numbers is in the ratio m : n then prove that the numbers are in the ratio (m+sqrt(m^2-n^2)):(m-sqrt(m^2-n^2))dot