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))`

If the A.M. and G.M. between two numbers are in the ratio x:y , then prove that the numbers are in the ratio (x+sqrt(x^(2)-y^(2))):(x-sqrt(x^(2)-y^(2))) .

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)).

If the A.M. and G.M. between two numbers are respectively 17 and 8, find the numbers.

If the ratio of H.M. and G.M. between two numbers a and b is 4:5 , then find the ratio of the two number ?

The A.M. and H.M. between two numbers are 27 and 12, respectively, then find their G.M.

The A.M. and H.M. between two numbers are 27 and 122, respectively, then find their G.M.

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)) .

If A and G be A.M. and GM., respectively between two positive numbers, prove that the numbers are A+-sqrt((A+G)(A-G)) .

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 .

Show that if A and G .are A.M. and G.M. between two positive numbers , then the numbers are A+- sqrt(A^(2) -G^(2))