Question

Find the fourth proportional to $$a^2$$, $$ab$$ and $$b^2$$.

Answer 1

Let the fourth proportional be $$x$$.

Then, $$\text{Product of extremes} = \text{Product of means}$$.

$$a^2 : ab :: b^2 : x$$

$$a^2 \times x = ab \times b^2 = ab^3$$

$$x = \frac{ab^3}{a^2} = \frac{b^3}{a}$$