\left\{ \begin{array} { l } { x y = 4 } \\ { 21 = x ^ { 2 } + y ^ { 2 } - \sqrt { 3 } x y } \end{array} \right.
Solve for x, y
x=-4\sqrt{-\frac{\sqrt{168\sqrt{3}+425}}{32}+\frac{\sqrt{3}}{8}+\frac{21}{32}}\approx -0.764956167\text{, }y=-\frac{\sqrt{2\sqrt{168\sqrt{3}+425}+8\sqrt{3}+42}}{2}\approx -5.229057782
x=4\sqrt{-\frac{\sqrt{168\sqrt{3}+425}}{32}+\frac{\sqrt{3}}{8}+\frac{21}{32}}\approx 0.764956167\text{, }y=\frac{\sqrt{2\sqrt{168\sqrt{3}+425}+8\sqrt{3}+42}}{2}\approx 5.229057782
x=-4\sqrt{\frac{2}{-\sqrt{168\sqrt{3}+425}+4\sqrt{3}+21}}\approx -5.229057782\text{, }y=-\frac{\sqrt{-2\sqrt{168\sqrt{3}+425}+8\sqrt{3}+42}}{2}\approx -0.764956167
x=4\sqrt{\frac{2}{-\sqrt{168\sqrt{3}+425}+4\sqrt{3}+21}}\approx 5.229057782\text{, }y=\frac{\sqrt{-2\sqrt{168\sqrt{3}+425}+8\sqrt{3}+42}}{2}\approx 0.764956167
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