求解 {l}{3x+6y=15}{y^2-sqrt{2}=-11}{x/2-z^3=4y}

$$\left.\begin{array} { l } { 3 x + 6 y = 15 } \\ { y ^ { 2 } - \sqrt { 2 } = - 11 } \\ { \frac { x } { 2 } - z ^ { 3 } = 4 y } \end{array} \right\}$$

求解 x, y, z 的值

$$x=5+2i\sqrt{11-\sqrt{2}}\approx 5+6.192184247i\text{, }y=-i\sqrt{11-\sqrt{2}}\approx -0-3.096092124i\text{, }z=\frac{\sqrt[3]{5}\times 2^{\frac{2}{3}}e^{\frac{i\arctan(2\sqrt{11-\sqrt{2}})}{3}}\sqrt[6]{45-4\sqrt{2}}}{2}\approx 2.231322913+1.134076773i$$

$$x=5+2i\sqrt{11-\sqrt{2}}\approx 5+6.192184247i\text{, }y=-i\sqrt{11-\sqrt{2}}\approx -0-3.096092124i\text{, }z=\frac{\sqrt[3]{5}\times 2^{\frac{2}{3}}e^{\frac{i\arctan(2\sqrt{11-\sqrt{2}})+2\pi i}{3}}\sqrt[6]{45-4\sqrt{2}}}{2}\approx -2.097800752+1.365343941i$$

$$x=5+2i\sqrt{11-\sqrt{2}}\approx 5+6.192184247i\text{, }y=-i\sqrt{11-\sqrt{2}}\approx -0-3.096092124i\text{, }z=\frac{\sqrt[3]{5}\times 2^{\frac{2}{3}}e^{\frac{i\arctan(2\sqrt{11-\sqrt{2}})+4\pi i}{3}}\sqrt[6]{45-4\sqrt{2}}}{2}\approx -0.133522162-2.499420713i$$

$$x=-2i\sqrt{11-\sqrt{2}}+5\approx 5-6.192184247i\text{, }y=i\sqrt{11-\sqrt{2}}\approx 3.096092124i\text{, }z=\frac{\sqrt[3]{5}\times 2^{\frac{2}{3}}e^{\frac{2\pi i-i\arctan(2\sqrt{11-\sqrt{2}})}{3}}\sqrt[6]{45-4\sqrt{2}}}{2}\approx -0.133522162+2.499420713i$$

$$x=-2i\sqrt{11-\sqrt{2}}+5\approx 5-6.192184247i\text{, }y=i\sqrt{11-\sqrt{2}}\approx 3.096092124i\text{, }z=\frac{\sqrt[3]{5}\times 2^{\frac{2}{3}}e^{\frac{4\pi i-i\arctan(2\sqrt{11-\sqrt{2}})}{3}}\sqrt[6]{45-4\sqrt{2}}}{2}\approx -2.097800752-1.365343941i$$

$$x=-2i\sqrt{11-\sqrt{2}}+5\approx 5-6.192184247i\text{, }y=i\sqrt{11-\sqrt{2}}\approx 3.096092124i\text{, }z=\frac{\sqrt[3]{5}\times 2^{\frac{2}{3}}e^{-\frac{i\arctan(2\sqrt{11-\sqrt{2}})}{3}}\sqrt[6]{45-4\sqrt{2}}}{2}\approx 2.231322913-1.134076773i$$