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.M and G.M of two positive numbers a and b 10 and 8 respectively , find the numbers ?

If the ratio of A.M. between two positive real numbers a and b to their H.M. is m:n then a:b is equal to :

The A.M and G.M of two numbers are in the ratio 3: 2, then the ratio of the numbers is

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

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

The ratio of the sums of m and n terms of an A.P is m^(2):n^(2) . Show that the ratio of m^(th) and n^(th) term is (2m-1) : (2n -1) .

If A,G and H are respectively A.M.,G.M. and H.M. of three positive numbers a,b and c, then the equation whose roots are a,b,c is given by :

Find two numbers whose A.M. is 5 and G.M. is 4.

If 12 and 9 are respectively A.M and G.M of two numbers, then the numbers are the roots of the equation