Решите систему уравнений.[latex] \left \{ {{x^2+2xy=16} \atop {y^2-xy=3}} \right. [/latex]

[latex] \left \{ {{x^2+2xy=16} \atop {y^2-xy=3}} \right. [/latex] [latex] x^2+2xy=16\\ 2y^2-2xy=6\\ \\ x^2+2y^2=22\\ x^2=22-2y^2\\ x=\sqrt{22-2y^2}\\ \\ 22-2y^2+2\sqrt{22-2y^2}y=16\\ -2y^2+2\sqrt{22-2y^2}y=-6\\ 2\sqrt{22-2y^2}*y=2y^2-6\\ 4y^2(22-2y^2)=4y^4-24y^2+36\\ 88y^2-8y^4=4y^4-24y^2+36\\ y=+-3\\ y=+-\frac{\sqrt{3}}{3}\\ x=+-2\\ x=+-\frac{8}{\sqrt{3}} [/latex]