Solve {l}{-5x^2+1xy+2y^2+4=0}{4x^2+4xy-4y^2-10=0}

$$\left. \begin{array} { l } { - 5 x ^ { 2 } + 1 x y + 2 y ^ { 2 } + 4 = 0 } \\ { 4 x ^ { 2 } + 4 x y - 4 y ^ { 2 } - 10 = 0 } \end{array} \right.$$

Solve for x, y (complex solution)

$$x=\frac{i\sqrt{246\sqrt{305}-3864}-i\sqrt{6\sqrt{305}-24}}{60}\approx 0.196691212i\text{, }y=-\frac{i\sqrt{6\sqrt{305}-24}}{6}\approx -0-1.498012528i$$

$$x=\frac{\sqrt{6\sqrt{305}+24}+\sqrt{246\sqrt{305}+3864}}{60}\approx 1.69470374\text{, }y=\frac{\sqrt{6\sqrt{305}+24}}{6}\approx 1.891394952$$

$$x=\frac{i\sqrt{6\sqrt{305}-24}-i\sqrt{246\sqrt{305}-3864}}{60}\approx -0.196691212i\text{, }y=\frac{i\sqrt{6\sqrt{305}-24}}{6}\approx 1.498012528i$$

$$x=\frac{-\sqrt{6\sqrt{305}+24}-\sqrt{246\sqrt{305}+3864}}{60}\approx -1.69470374\text{, }y=-\frac{\sqrt{6\sqrt{305}+24}}{6}\approx -1.891394952$$

Solve for x, y

$$x=\frac{\sqrt{6}\left(\sqrt{\sqrt{305}+4}+\sqrt{41\sqrt{305}+644}\right)}{60}\approx 1.69470374\text{, }y=\frac{\sqrt{6\left(\sqrt{305}+4\right)}}{6}\approx 1.891394952$$

$$x=-\frac{\sqrt{6}\left(\sqrt{\sqrt{305}+4}+\sqrt{41\sqrt{305}+644}\right)}{60}\approx -1.69470374\text{, }y=-\frac{\sqrt{6\left(\sqrt{305}+4\right)}}{6}\approx -1.891394952$$