If `a` is the A.M. of `ba n dc` and the two geometric means are `G_1a n dG_2` , then prove that `G1 3+G2 3=2a b cdot`

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)=2ab

If a is the A.M.of b and c and the two geometric means are G_(1) and G_(2), then prove that G_(1)^(3)+G_(2)^(3)=2abc.

If a be one A.M and G_(1) and G_(2) be then geometric means between b and c then G_(1)^(3)+G_(2)^(3)=

If a is A.M. of b and c and c, G_(1) , G_(2) ,b are in G.P., then find the value of G_(1)^(3)+G_(2)^(3)-2abc

If one A.M.A and tow geometric means G_(1) and G_(2) inserted between any two positive numbers,show that (G_(1)^(1))/(G_(2))+(G_(2)^(2))/(G_(1))=2A

If G is the geometric mean of x and y then prove that (1)/(G^(2)-x^(2))+(1)/(G^(2)-y^(2))=(1)/(G^(2))

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