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 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

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 one geometric mean G and two arithmetic means p,q be inserted between two given numbers,then prove that,G^(2)=(2p-q)(2q-p)

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

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

If G_1 and G_2 are two geometric means and A the asrithmetic mean inserted between two numbers, then the value of G_1^2/G_2+G_2^2/G_1 is (A) A/2 (B) A (C) 2A (D) none of these

If one geometric mean G and two arithmetic means A_(1) and A_(2) be inserted between two given quantities,prove that G^(2)=(2A_(1)-A_(2))(2A_(2)-A_(1))

If one geometric mean G and two arithmetic means A_(1)andA_(2) are inserted between two given quantities, then (2A_(1)-A_(2))(2A_(2)-A_(1))=