$$\left. \begin{array} { l } { x ^ { 2 } + \frac { 1 } { 2 } = 2 } \\ { 27 x ^ { 3 } + 1 } \\ { 27 x ^ { 2 } + \frac { 1 } { 27 x } } \end{array} \right.$$
$x=\frac{\sqrt{6}}{2}\approx 1.224744871\text{, }y=\frac{81\sqrt{6}}{4}+1\approx 50.602167291\text{, }z=\frac{\sqrt{6}}{81}+\frac{81}{2}\approx 40.530240614$
$x=-\frac{\sqrt{6}}{2}\approx -1.224744871\text{, }y=-\frac{81\sqrt{6}}{4}+1\approx -48.602167291\text{, }z=-\frac{\sqrt{6}}{81}+\frac{81}{2}\approx 40.469759386$
