Question

$(x-4)$ is geometric mean of $(x-5)$ and $(x-2)$, find the value of $x$.

Answer 1

Geometric mean of two numbers, $a$ and $b$ is $\sqrt{ab}$
So, geometric mean of $(x-5),(x-2)$ is $\sqrt{(x-5)\times (x-2)}=(x-4)$

Squaring both sides,

$x^2-5x-2x+10=x^2-8x+16$

$-7x+8x=16-10$

$x=6$