Let A,G,H be the arithmetic, geometric and harmonic means between three given no. a,b,c then the equation having a,b,c as its root is `x^3-3Ax^2+3G^3/H x-G^3=0`

Let A;G;H be the arithmetic; geometric and harmonic means of two positive no.a and b then A>=G>=H

If A and G are respectively arithmetic and geometric mean between positive no. a and b ; then the quadratic equation having a,b as its roots is x^2-2Ax+G^2=0.

If A, G and H are the arithmetic, geometric and harmonic means between a and b respectively, then which one of the following relations is correct?

If A,G and H are the arithmetic mean, geometric mean and harmonic mean between unequal positive integers.Then,the equation Ax^(2)-IGlx-H=0 has (a) both roots are fractions (b) atleast one root which is negatuve fraction ( c) exactly one positive root (d) atleast one root which is an integer

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_(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 3 arithmetic means, 3 geometric means and 3 harmonic means are inserted between 1 and 5, then the cubic equation whose roots are first A.M., second G.M. and third H.M. between 1 and 5, is

If a be the arithmetic mean and b, c be the two geometric means between any two positive numbers, then (b^3 + c^3) / abc equals

Let a_1,a_2,a_3…………., a_n be positive numbers in G.P. For each n let A_n, G_n, H_n be respectively the arithmetic mean geometric mean and harmonic mean of a_1,a_2,……..,a_n On the basis of above information answer the following question: A_k,G_k,H_k are in (A) A.P. (B) G.P. (C) H.P. (D) none of these

Statement-l: a and b are two numbers and A ,G,H represents Arthmetic,Geometric and Harmonic means between a and b.If A-G=(3)/(2) and G-H=(6)/(5) then the numbers are 24 and 6. Statement-II: The Arithmetic,Geometric and Harmonic means between a and b is (a+b)/(2),sqrt(ab) and (2ab)/(a+b)