Problem 2. II variant.

Solve the system of equations $\left\{\begin{array}{l}x+y+\sqrt{z}=4, \\ \sqrt{x} \sqrt{y}-\sqrt{w}=2 .\end{array}\right.$

Solution. $\left\{\begin{array}{l}(\sqrt{x})^{2}+(\sqrt{y})^{2}+\sqrt{z}=4, \\ 2 \sqrt{x} \sqrt{y}-2 \sqrt{w}=4\end{array} \Rightarrow(\sqrt{x}-\sqrt{y})^{2}+\sqrt{z}+2 \sqrt{w}=0\right.$.

From this $\left\{\begin{array}{l}x=y, \\ z=w=0 .\end{array}\right.$

From the equation $x+y=4$ we find $x=y=2$.
Answer: $(x ; y ; z ; w) \in\{(2 ; 2 ; 0 ; 0)\}$.