Solve {l}{sqrt{3}a^2-13b^2-2ab=0}{a^2+b^2=1}

$$\left\{ \begin{array} { l } { \sqrt { 3 } a ^ { 2 } - 13 b ^ { 2 } - 2 a b = 0 } \\ { a ^ { 2 } + b ^ { 2 } = 1 } \end{array} \right.$$

Solve for a, b

$$a=-\frac{-\sqrt{13\sqrt{3}+1}+1}{\sqrt{-2\sqrt{13\sqrt{3}+1}+13\sqrt{3}+5}}\approx 0.911937309\text{, }b=-\sqrt{\frac{3}{-2\sqrt{13\sqrt{3}+1}+13\sqrt{3}+5}}\approx -0.410329556$$

$$a=\frac{-\sqrt{13\sqrt{3}+1}+1}{\sqrt{-2\sqrt{13\sqrt{3}+1}+13\sqrt{3}+5}}\approx -0.911937309\text{, }b=\sqrt{\frac{3}{-2\sqrt{13\sqrt{3}+1}+13\sqrt{3}+5}}\approx 0.410329556$$

$$a=-\frac{\sqrt{13\sqrt{3}+1}+1}{\sqrt{2\sqrt{13\sqrt{3}+1}+13\sqrt{3}+5}}\approx -0.958847398\text{, }b=-\sqrt{\frac{3}{2\sqrt{13\sqrt{3}+1}+13\sqrt{3}+5}}\approx -0.283921939$$

$$a=\frac{\sqrt{13\sqrt{3}+1}+1}{\sqrt{2\sqrt{13\sqrt{3}+1}+13\sqrt{3}+5}}\approx 0.958847398\text{, }b=\sqrt{\frac{3}{2\sqrt{13\sqrt{3}+1}+13\sqrt{3}+5}}\approx 0.283921939$$