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 cdot`

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 , b ,c are three distinct positive real numbers in G.P., then prove that c^2+2a b >3a cdot

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 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

G is the geometric mean and p and q are two arithmetic means between two numbers a and b, prove that : G^(2)=(2p-q)(2q-p)

If a is the A.M. between b and c, b the G.M. between a and c, then show that 1/a,1/c,1/b are in A.P.

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