\left\{ \begin{array} { l } { 2 x - y + 2 x \lambda + \lambda y = 0 } \\ { - x + 2 y + \lambda x + 2 y \lambda = 0 } \\ { x ^ { 2 } + x y + y ^ { 2 } - 3 = 0 } \end{array} \right.
Solve for x, y, λ
x=-\sqrt{3}\approx -1.732050808\text{, }y=\sqrt{3}\approx 1.732050808\text{, }\lambda =-3
x=-1\text{, }y=-1\text{, }\lambda =-\frac{1}{3}\approx -0.333333333
x=\sqrt{3}\approx 1.732050808\text{, }y=-\sqrt{3}\approx -1.732050808\text{, }\lambda =-3
x=1\text{, }y=1\text{, }\lambda =-\frac{1}{3}\approx -0.333333333
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