Solve y=sqrt{x}+2/sqrt{x}

$$y = \sqrt { x } + \frac { 2 } { \sqrt { x } }$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\left(-\sqrt{y^{2}-8}+y\right)^{2}}{4}\text{, }&arg(\frac{-\sqrt{y^{2}-8}+y}{2})<\pi \\x=\frac{\left(\sqrt{y^{2}-8}+y\right)^{2}}{4}\text{, }&arg(\frac{\sqrt{y^{2}-8}+y}{2})<\pi \end{matrix}\right.$$

Solve for y (complex solution)

$$y=x^{-\frac{1}{2}}\left(x+2\right)$$

$$x\neq 0$$

Solve for x

$$x=\frac{\left(-\sqrt{y^{2}-8}+y\right)^{2}}{4}$$

$$x=\frac{\left(\sqrt{y^{2}-8}+y\right)^{2}}{4}\text{, }y\geq 2\sqrt{2}$$

Solve for y

$$y=\frac{x+2}{\sqrt{x}}$$

$$x>0$$