Question

If x, y and z are the arithmetic, geometric and harmonic means of two positive numbers respectively .Then the relation between x, y and z is

• A. $xz=y^2$
• B. $xy=z^2$
• C. $xy=z$
• D. $xz=y^4$

Answer 1

The correct option is A

$xz=y^2$

Let the two positive numbers be a and b.
A.M. of the two numbers is $\frac{(a+b)}{2}$
H.M. of the two numbers is $\frac{2ab}{a+b}$
G.M. of the two numbers is (ab) $\left(\frac{1}{2}\right)$
The relation is $(A.M.)\times (\times (H.M.)=(G.M.)2$
xz = y2