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) . G_(2) , g_(3) are three geometric means between two positive numbers a and b , then g_(1) g_(3) is equal to

If a,b,c,d are four distinct positive numbers in G.P.then show that a+d>b+c.

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 .

Let G be the geometric mean of two positive numbers a and b, and M be the arithmetic mean of 1/a and 1/b if 1/M:G is 4:5, then a:b can be

G_(1),G_(2),G_(3),G_(4) are the geometric means between positive numbers a and b then the quadratic equation (G_(1)+G_(3))G_(2)G_(3)x^(2)-G_(2)x-(G_(1)+G_(3))G_(1)G_(4)=0 has roots which are

If A_(1),A_(2),A_(3);G_(1),G_(2),G_(3); and H_(1),H_(2),H_(3) are the three arithmetic,geometric and harmonic means between two positive numbers a and b(a>b), then which of the following is (are) true?

If A_(1) , A_(2) , A_(3) , G_(1) , G_(2) , G_(3) , and H_(1) , H_(2) , H_(3) are the three arithmetic, geometric and harmonic means between two positive numbers a and b(a gt b) , then which of the following is/are true ?

If A and G be the A .M and G.M between two positive numbers, then the numbers are

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)

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