Solve {l}{x^4+x^-4=194220}{y=(x-2)^2}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { x ^ {4} + x ^ {-4} = 194220 }\\ { y = {(x - 2)} ^ {2} }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Solve for x, y, z

$$x=-\frac{\sqrt{2\left(\sqrt{194222}-19\sqrt{538}\right)}}{2}\approx -0.047635038\text{, }y=\frac{4\sqrt{2\left(\sqrt{194222}-19\sqrt{538}\right)}+\sqrt{194222}+8-19\sqrt{538}}{2}\approx 4.192809247\text{, }z=\frac{4\sqrt{2\left(\sqrt{194222}-19\sqrt{538}\right)}+\sqrt{194222}+8-19\sqrt{538}}{2}\approx 4.192809247$$

$$x=\frac{\sqrt{2\left(\sqrt{194222}-19\sqrt{538}\right)}}{2}\approx 0.047635038\text{, }y=\frac{-4\sqrt{2\left(\sqrt{194222}-19\sqrt{538}\right)}+\sqrt{194222}+8-19\sqrt{538}}{2}\approx 3.811728946\text{, }z=\frac{-4\sqrt{2\left(\sqrt{194222}-19\sqrt{538}\right)}+\sqrt{194222}+8-19\sqrt{538}}{2}\approx 3.811728946$$

$$x=-\frac{\sqrt{2\left(\sqrt{194222}+19\sqrt{538}\right)}}{2}\approx -20.992950776\text{, }y=\frac{4\sqrt{2\left(\sqrt{194222}+19\sqrt{538}\right)}+\sqrt{194222}+19\sqrt{538}+8}{2}\approx 528.67578538\text{, }z=\frac{4\sqrt{2\left(\sqrt{194222}+19\sqrt{538}\right)}+\sqrt{194222}+19\sqrt{538}+8}{2}\approx 528.67578538$$

$$x=\frac{\sqrt{2\left(\sqrt{194222}+19\sqrt{538}\right)}}{2}\approx 20.992950776\text{, }y=\frac{-4\sqrt{2\left(\sqrt{194222}+19\sqrt{538}\right)}+\sqrt{194222}+19\sqrt{538}+8}{2}\approx 360.732179174\text{, }z=\frac{-4\sqrt{2\left(\sqrt{194222}+19\sqrt{538}\right)}+\sqrt{194222}+19\sqrt{538}+8}{2}\approx 360.732179174$$