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))`.

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))

If A and G are the arithmetic and geometric means respectively of two numbers then prove that the numbers are (A+sqrt(A^(2)-G^(2)))and(A-sqrt(A^(2)-G^(2)))

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

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

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

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 one G.M., G and two A.M's p and q be inserted between two given numbers, prove that G^(2)= (2p-q) (2q-p)

If HM:GM=4:5 for two positive numbers, then the ratio of two numbers is -

If A.M. and GM. of two positive numbers a and b are 10 and 8, respectively find the numbers.