If one A.M., `A` and two geometric means `G_1a n dG_2` inserted between any two positive numbers, show that `(G1 ^2)/(G2)+(G2 ^2)/(G_1)=2Adot`

If one geometric mean G and two arithmetic means A_1a n dA_2 be inserted between two given quantities, prove that G^2=(2A_1-A_2)(2A_2-A_1)dot

If one A.M. A and two G.M.\'s p and q be inserted between two given numbers, shwo that p^2/q+q^2/p=2A

If one G.M., G and two A.M's p and q be inserted between two given numbers, prove that G^(2)= (2p-q) (2q-p)

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 .

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

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 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=

Show that if A and G .are A.M. and G.M. between two positive numbers , then the numbers are A+- sqrt(A^(2) -G^(2))

If G_(1) is the first of n G.M. s between positive numbers a and b , then show that G_(1)^(n+1) = a^(n) b .