Vyriešiť x-y/sqrt{x-sqrt{y}}-sqrt{x}=z

$$\frac{ x-y }{ \sqrt{ x } - \sqrt{ y } } - \sqrt{ x } =z$$

Riešenie pre x (complex solution)

$$x\neq y$$

$$z=\sqrt{y}$$

Riešenie pre y (complex solution)

$$y=z^{2}$$

$$\left(x\neq z^{2}\text{ and }z\neq \sqrt{x}\text{ and }arg(z)<\pi \text{ and }z\neq 0\right)\text{ or }\left(z=0\text{ and }x\neq 0\right)$$

Riešenie pre x

$$\left\{\begin{matrix}x\in [0,z^{2})\text{, }&z>0\text{ and }y=z^{2}\\x>z^{2}\text{, }&z\geq 0\text{ and }y=z^{2}\\x>0\text{, }&z=0\text{ and }y=0\end{matrix}\right,$$

Riešenie pre y

$$y=z^{2}$$

$$z\geq 0\text{ and }x\geq 0\text{ and }x\neq z^{2}$$