Question

The mean proportional of x and y is z. What is the mean proportional of x²z and y²z?

• A. yz²
• B. xz²
• C. z³
• D. z

Answer 1

Answer:

C. z³

The mean proportional between two numbers (a) and (b) is (\sqrt{ab}).

Given:
Mean proportional of (x) and (y) is (z), so
$z = \sqrt{xy}$

Squaring both sides:
$z^2 = xy$

Now we need the mean proportional of (x^2 z) and (y^2 z):

$= \sqrt{(x^2 z)(y^2 z)}$

$= \sqrt{x^2 y^2 z^2}$

= xyz

Now substitute (xy = z^2):

$xyz = z^2 \cdot z = z^3$
Final Answer:

$\boxed{z^3}$