If A, G, H be respectively the A M, G M, and H . M between two positive numbers if x A=y G=z H where x, y, z are non-zero positive real number then x, y, z are in

Question

If A, G, H be respectively the A M, G M, and H . M between two positive numbers if x A=y G=z H where x, y, z are non-zero positive real number then x, y, z are in (A) A.P. (B) G.P. (C) H.P. (D) Data insufficient

Tardigrade Admin · Accepted Answer

Let number are a and b then A =( a + b /2), G =√a b text and H =(2 a b/a+b) x A =y G ⇒ (x/y)=(2 √a b/a+b) also y G=z H ⇒ (y/z)=(2 √a b/a+b) ⇒ (x/y)=(y/z) Hence vr x, y, z are in GP

Q. If $A, G, H$ be respectively the $A M, GM$ , and $H . M$ between two positive numbers if $x A = y G = zH$ where $x, y, z$ are non-zero positive real number then $x, y, z$ are in

A.P.

G.P.

H.P.

Data insufficient

Let number are $a$ and $b$ then
$A = \frac{a + b}{2},$
$G = ab and H = \frac{2 ab}{a + b}$
$x A = y G \Rightarrow \frac{x}{y} = \frac{2 ab}{a + b}$
also $y G = zH \Rightarrow \frac{y}{z} = \frac{2 ab}{a + b}$
$\Rightarrow \frac{x}{y} = \frac{y}{z}$ Hence vr $x, y, z$ are in GP

Q. If A,G,H be respectively the AM,GM, and H.M between two positive numbers if xA=yG=zH where x,y,z are non-zero positive real number then x,y,z are in