Question

If $(28-x)$ is the mean proportional of $(23-x)$ and $(19-x)$ find the value of $x$.

Answer 1

$(28-x)$ is the mean proportional of $(23-x)$ and $(19-x)$

$\therefore \frac{23-x}{28-x}=\frac{28-x}{19-x}$

$\therefore \frac{(23-x)-(28-x)}{28-x}=\frac{(28-x)-(19-x)}{19-x}$ by dividendo

$\Rightarrow \frac{-5}{28-x}=\frac{9}{19-x}$

$\Rightarrow -5(19-x)=9(28-x)$

$\Rightarrow -95+5x=252-9x$

$\Rightarrow 14x=347$

$\therefore x=\frac{347}{14}$