If A and G are the AM and GM of the positive number a and b then prove that `AgeG`

If A and G be the A.M. and G.M. of two numbers a and b and A:G=m:n ,then prove that- a:b=m+sqrt(m^2-n^2) :m-sqrt(m^2-n^2)

The A.M. and G.M. of two positive numbers are 25 and 24 respectively. Find them.

The A.M. and G.M. of two positive numbers are 15 and 9 respectively. Find them.

If a and b are two odd positive integers such that a>b. Then prove that one of the two numbers (a+b)/2 and (a-b)/2 is odd and other is even.

If the arithmetic and geometriv means of two positive numbers are A and G respectively,then show that AgeG .

The sum of A.M. and G.M. of two positive numbers is 32 and the ratio of these two numbers is 1:9. Find them.

The sum of A.M. and G.M. of two positive numbers is 96 and the ratio of the two numbers is 1:9. Find them.

The A.M. of two positive numbers a and b is twice their G.M. Prove that - a:b=2+sqrt3:2-sqrt3 .

If a and b are two unequal positive real numbers,then prove that (a+b)(5/a+1/(5b))gt4 .

a, b, c are in A.P. If x be the G.M. of a and b, and y be the G.M. of b and c, then prove that b^2 is the A.M. of x_2 and y_2 .