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 .

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 .

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 .

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 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 A and G are the A.M.and G.M. of two unequal positive numbers a and b, show that A>G>G^2/A

If A_(1),A_(2) are two A.M.'s and G_(1),G_(2) be two G.M.'s between two positive numbers a and b, then (A_(1)+A_(2))/(G_(1)G_(2)) is equal to (i) (a+b)/(ab) (ii) (a+b)/2 (iii) (a+)/(a-b) (iv) None of these

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 G be the GM between x and y, then the value of (1)/(G^(2)-x^(2))+(1)/(G^(2)-y^(2)) is equal to (A)G^(2)(B)(2)/(G^(2))(C)(1)/(G^(2))(D)3G^(2)

If m be the A.M. and g be the G.M. of two positive numbers 'a' and 'b' such that m:g=1:2 , then (a)/(b) can be equal to