Solve {l}{x^{2}+y^2=z^2}{z=sqrt{3}}{y=x^2-e^2+z}

$$\left. \begin{array} { l } { x ^ { 2 } + y ^ { 2 } = z ^ { 2 } } \\ { z = \sqrt { 3 } } \\ { y = x ^ { 2 } - e ^ { 2 } + z } \end{array} \right.$$

Solve for x, y, z

$$x=e^{\frac{-i\arctan(\frac{\sqrt{4e^{2}-4\sqrt{3}-13}}{2e^{2}-2\sqrt{3}-1})+2\pi i}{2}}\sqrt{|\frac{-\left(1+i\sqrt{4e^{2}-4\sqrt{3}-13}\right)^{2}+12}{4}|}\approx -2.295901649+0.337874368i\text{, }y=\frac{-i\sqrt{4e^{2}-4\sqrt{3}-13}-1}{2}\approx -0.5-1.551452639i\text{, }z=\sqrt{3}\approx 1.732050808$$

$$x=e^{-\frac{i\arctan(\frac{\sqrt{4e^{2}-4\sqrt{3}-13}}{2e^{2}-2\sqrt{3}-1})}{2}}\sqrt{|\frac{-\left(1+i\sqrt{4e^{2}-4\sqrt{3}-13}\right)^{2}+12}{4}|}\approx 2.295901649-0.337874368i\text{, }y=\frac{-i\sqrt{4e^{2}-4\sqrt{3}-13}-1}{2}\approx -0.5-1.551452639i\text{, }z=\sqrt{3}\approx 1.732050808$$

$$x=e^{\frac{i\arctan(\frac{\sqrt{4e^{2}-4\sqrt{3}-13}}{2e^{2}-2\sqrt{3}-1})}{2}}\sqrt{|\frac{2e^{2}-2\sqrt{3}-1+i\sqrt{4e^{2}-4\sqrt{3}-13}}{2}|}\approx 2.295901649+0.337874368i\text{, }y=\frac{-1+i\sqrt{4e^{2}-4\sqrt{3}-13}}{2}\approx -0.5+1.551452639i\text{, }z=\sqrt{3}\approx 1.732050808$$

$$x=e^{\frac{i\arctan(\frac{\sqrt{4e^{2}-4\sqrt{3}-13}}{2e^{2}-2\sqrt{3}-1})+2\pi i}{2}}\sqrt{|\frac{-\left(-1+i\sqrt{4e^{2}-4\sqrt{3}-13}\right)^{2}+12}{4}|}\approx -2.295901649-0.337874368i\text{, }y=\frac{-1+i\sqrt{4e^{2}-4\sqrt{3}-13}}{2}\approx -0.5+1.551452639i\text{, }z=\sqrt{3}\approx 1.732050808$$