Question

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

Answer 1

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

i.e., $(23-x)(19-x)=(28-x{)}^2$

$x^2-42x+437=784-56x+x^2$

$56x-42x=784-437$

$14x=347$

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