\left\{ \begin{array} { l } { 2 x ( 1 + \lambda ) + \mu = 0 } \\ { 2 z - \lambda - \mu = 0 } \\ { 2 x ^ { 2 } - z = 0 } \\ { 2 x + z - 1 = 0 } \end{array} \right.
Solve for x, λ, μ, z
x=\frac{-\sqrt{3}-1}{2}\approx -1.366025404\text{, }z=\sqrt{3}+2\approx 3.732050808\text{, }\lambda =3-\sqrt{3}\approx 1.267949192\text{, }\mu =3\sqrt{3}+1\approx 6.196152423
x=\frac{\sqrt{3}-1}{2}\approx 0.366025404\text{, }z=2-\sqrt{3}\approx 0.267949192\text{, }\lambda =\sqrt{3}+3\approx 4.732050808\text{, }\mu =1-3\sqrt{3}\approx -4.196152423
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