If one A.M., `A` and tow geometric means `G_1a n dG_2` inserted between any two positive numbers, show that `(G1 2)/(G_2)+(G2 2)/(G_1)=2Adot`

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 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 one G.M. 'G' and two arithmetic means p and q be inserted between any two given number than G^(2) =

If G is the G.M between two positive numbers a and b.show that 1/(G^2-a^2)+1/(G^2-b^2)=1/G^2

If G_1 ,G_2 are geometric means , and A is the arithmetic mean between two positive no. then show that G_1^2/G_2+G_2^2/G_1=2A .

Let 3 geometric means G_(1),G_(2),G_(3) are inserted between two positive number a and b such that (G_(3)-G_(2))/(G_(2)-G_(1))=2 then (b)/(a) equal to (i)2 (ii) 4 (iii) 8 (iv) 16

If A is the arithmatic mean and G_(1) and G_(2) be two geometric means between any two numbers then prove that, (G_(1)^(2))/(G_(2)) + (G_(2)^(2))/(G_(1))=2A

If G is the G.M. between two positive numbers a and b, show that (1)/(G^(2) - a^(2)) + (1)/(G^(2) - b^(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