Question

If $x$ is the geometric mean of $(x+2)$ and $(x-1)$, then find the value of $x$.

Answer 1

$G=\pm \sqrt{ab},$ Here $G=x$
$\therefore x=\pm \sqrt{(x+2)(x-1)}$
$\therefore x^2=(x+2)(x-1)$ (Squaring on both sides)
$\therefore x^2=x^2+x-2$
$\therefore x-2=0$
$\therefore x=2$.