$\begin{array}{l}1)\quad A = \dfrac{2}{2+\sqrt5} + \dfrac{2}{2 - \sqrt5}\\ \to A = \dfrac{2(2-\sqrt5)}{(2+\sqrt5)(2-\sqrt5)}+ \dfrac{2(2+\sqrt5)}{(2+\sqrt5)(2-\sqrt5)}\\ \to A = \dfrac{2(2 - \sqrt5 + 2 + \sqrt5)}{4 -5}\\ \to A = \dfrac{2.4}{-1}\\ \to A = -8\\ 2)\quad \begin{cases}x+ y^2 = 6\\-5x + y = -8\qquad (*)\end{cases}\\ \to \begin{cases}5x+ 5y^2 = 30\\-5x + y = -8\end{cases}\\ \to 5y^2 + y =22\\ \to 5y^2 + y - 22 =0\\ \to \left[\begin{array}{l}y = 2\\y = -\dfrac{11}{5}\end{array}\right.\\ +)\quad y = 2\\ \to (*) \Leftrightarrow -5x + 2 = -8\Leftrightarrow x = 2\\ +) \quad y = -\dfrac{11}{5}\\ \to (*) \Leftrightarrow -5x -\dfrac{11}{5} = -8\Leftrightarrow x = \dfrac{29}{25}\\ \text{Vậy hệ phương trình có nghiệm}\,\,(x;y)=\left\{(2;2);\left(\dfrac{29}{25};-\dfrac{11}{5}\right) \right\} \end{array}$
