If A and G are the A.M. and G.M. respectively between any two distinct positive numbers a and b then show that A > G.

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

If G is the geometric mean between two distinct positive numbers a and b, then show that 1/(G-a)+1/(G-b)=1/G .

The A.M. between two positive numbers is 34 and their G.M. is 16. find the numbers.

Let A_(1),G_(1),H_(1) denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For nge2 , let A_(n-1),G_(n-1)" and "H_(n-1) has arithmetic,geometric and harmonic means as A_(n),G_(n),H_(n) respectively. Which of the following statement is correct?

The A.M. between two distinct positive numbers is twice the G.M. between them. Find the ratio of the greater to the smaller.

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,b,c are in AP and p is the AM between a and b and q is the AM between b and c, then show that b is the AM between p and q.

If A.M and G.M of two positive numbers are 13 and 12 respectively. Find the numbers.

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)))