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 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) .

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 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))

Show that the following numbers are irrational. (i) 6+sqrt(2) (ii) 3-sqrt(5)

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))) .

find the value of ( 3 + sqrt3 ) xx ( 2 + sqrt2 )

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