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`

If the arithmetic means of two positive number a and b (a gt b ) is twice their geometric mean, then find the ratio a: b

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)) .

The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio (3+2sqrt2):(3-2sqrt2)

If H_(1) , H_(2) are two harmonic means between two positive numbers a and b , (a != b) , A and G are the arithmetic and geometric means between a and b , then (H_(2) + H_(1))/(H_(2) H_(1)) is

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

The arithmetic mean of two positive numbers is 6 and their geometric mean G and harmonic mean H satisfy the relation G^(2)+3H=48 . Then the product of the two numbers is

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)):sqrt((m-m^2-n^2))dot

If m is the A.M. of two distinct real numbers l and n""(""l ,""n"">""1) and G1, G2 and G3 are three geometric means between l and n, then G1 4+2G2 4+G3 4 equals, (1) 4l^2 mn (2) 4l^m^2 mn (3) 4l m n^2 (4) 4l^2m^2n^2

Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(1-3sqrt(2)x)^9dot