If $x - \sqrt{ \frac{2}{x} } = 3 $ then $x-\sqrt{2x} = ?$ Please find the value without calculate the value of $x$. I tried to multipy it by $x$, I tried to square it but I still can't find the solution. I tried to make some equation that my help to solve this:
$$x^{2} + \frac{2}{x}-2\sqrt{2x} =9, $$
$$x^{2} - \sqrt{2x} = 3x,$$
$$x^2 - \frac{2}{x} = 3\left(x+\sqrt{\frac{2}{x}}\right).$$

Let $\sqrt{\dfrac x2}=y\implies x=2y^2$
$$\implies2y^2-\dfrac1y=3\iff2y^3-3y-1=0$$
Let $x-\sqrt{2x}=2y^2-2y=2a,y^2-y-a=0\ \ \ \ (1)$
$2y-\dfrac1y=3-2a\iff2y^2+(2a-3)y-1=0\ \ \ \ (2)$
$(1),(2)$ will represent the same equation iff $$\dfrac12=\dfrac{-1}{2a-3}=\dfrac a1$$
Clearly $2a=?$
