If three quantities are in continued proportion; show that the ratio of the first to third is duplicate ratio of first to the second.

Find the third proportional to $\dfrac{x}{y} + \dfrac{y}{x} \text{ and } \sqrt{x^2 + y^2}$

If p + r = mq and $\dfrac{1}{q} + \dfrac{1}{s} = \dfrac{m}{r};$ then prove that : p : q = r : s.

If x + y + z = 0, the value of $\dfrac{x}{y + z}$ is :

1. 2

2. $\dfrac{1}{2}$

3. 1

4. -1