Solve {c}{2x+y+z^2=10}{x-y=10}{yz=5}

$$\left. \begin{array} { c } { 2 x + y + z ^ { 2 } = 10 } \\ { x - y = 10 } \\ { y z = 5 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{-\sqrt[3]{18} \cdot 5 ^ {\frac{2}{3}} {({(\sqrt{1209} + 27)} ^ {\frac{2}{3}} + {(\sqrt{1209} - 27)} ^ {\frac{2}{3}} - 4 \sqrt[3]{60})} + 360}{54} \approx 6.114643794$$

$$y=\frac{-\sqrt[3]{18}\times 5^{\frac{2}{3}}\left(\left(\sqrt{1209}+27\right)^{\frac{2}{3}}+\left(\sqrt{1209}-27\right)^{\frac{2}{3}}-4\sqrt[3]{60}\right)-180}{54}\approx -3.885356206$$

$$z=\frac{\sqrt[3]{5}\times 18^{\frac{2}{3}}\left(\sqrt[3]{\sqrt{1209}-27}-\sqrt[3]{\sqrt{1209}+27}\right)}{18}\approx -1.286883296$$