\left\{ \begin{array} { l } { \frac { 1 } { x } + 2 \lambda x = 0 } \\ { \frac { 1 } { y } + 2 \lambda y = 0 } \\ { \frac { 3 } { z } + 2 \lambda z = 0 } \\ { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 5 } \end{array} \right.
Solve for x, λ, y, z
x=1\text{, }y=1\text{, }z=-\sqrt{3}\approx -1.732050808\text{, }\lambda =-\frac{1}{2}=-0.5
x=-1\text{, }y=-1\text{, }z=\sqrt{3}\approx 1.732050808\text{, }\lambda =-\frac{1}{2}=-0.5
x=1\text{, }y=-1\text{, }z=-\sqrt{3}\approx -1.732050808\text{, }\lambda =-\frac{1}{2}=-0.5
x=-1\text{, }y=1\text{, }z=\sqrt{3}\approx 1.732050808\text{, }\lambda =-\frac{1}{2}=-0.5
x=-1\text{, }y=1\text{, }z=-\sqrt{3}\approx -1.732050808\text{, }\lambda =-\frac{1}{2}=-0.5
x=1\text{, }y=-1\text{, }z=\sqrt{3}\approx 1.732050808\text{, }\lambda =-\frac{1}{2}=-0.5
x=-1\text{, }y=-1\text{, }z=-\sqrt{3}\approx -1.732050808\text{, }\lambda =-\frac{1}{2}=-0.5
x=1\text{, }y=1\text{, }z=\sqrt{3}\approx 1.732050808\text{, }\lambda =-\frac{1}{2}=-0.5
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