The A.M. between two numbers b and c is a and the two G.Ms is `g_1` and `g_2` If `g_1^3+g_2^3=kabc` then find the value of k

If the A.M. between two positive numbers exceeds their G.M. by 2 and the ratio of the numbers be 1: 4 find the numbers .

If the A.M. between two positive numbers exceeds their G.M. by 2 and the ratio of the numbers be 1: 4 find the numbers .

If A_1 and A_2 are two A.M.s between a and b and G_1 and G_2 are two G.M.s between the same numbers then what is the value of (A_1+A_2)/(G_1G_2)

If A_(1) and A_(2) are two A.M.s between a and b and G_(1) and G_(2) are two G.M.s between the same numbers then what is the value of (A_(1)+A_(2))/(G_(1)G_(2))

If a is the A.M. of b and c and the two geometric mean are G_1 and G_2, then prove that G_1^3+G_2^3=2a b c

If A and G are A.M and G.M between two positive numbers a and b are connected by the relation A+ G = a- b then the numbers are in the ratio

If G_1 and G_2 are two geometric means inserted between any two numbers and A is the arithmetic mean of two numbers, then the value of (G_1^2)/G_2+(G_2^2)/G_1 is:

If a is the arithmetic mean of b and c, and two geometric means G_(1) and G_(2) are inserted between b and c such that G_(1)^(3)+G_(2)^(3)=lamda abc, then find the value of lamda .