1043 система. Как решить задачу

[latex] \left \{ {{ \sqrt[3]{x} +\sqrt[3]{y}=1 } \atop {xy=-8}} \right. \; \left \{ {{( \sqrt[3]{x}+ \sqrt[3]{y} )^3=1^3} \atop {xy=-8}} \right. \; \left \{ {{x+y+3\sqrt[3]{xy}\cdot (\sqrt[3]{x}+\sqrt[3]{y})=1} \atop {x=2}} \right. \\\\ \left \{ {{x+y+3\cdot \sqrt[3]{-8}\cdot 1=1} \atop {xy=-8}} \right. \; \left \{ {{x+y=7} \atop {xy=-8}} \right. \; \left \{ {{y=7-x} \atop {x(7-x)=-8}} \right. [/latex] [latex]-x^2+7x+8=0\; ,\; x^2-7x-8=0\; ,\; x_1=-1,\; x_2=8\\\\ \left \{ {{x_1=-1,\; x_2=8} \atop {y_1=8,\; y_2=-1}} \right. [/latex] [latex]Otvet:\; \; (-1,8)\; ,\; \; (8,-1)\; .[/latex]