Question

Решите систему с полным основанием $\left \{ {{x-y^{2}=6 } \atop {xy^{2}=7 }} \right.$

Answer 1

$\left \{ {{x-y^{2}=6 } \atop {xy^{2} =7}} \right. \\\\\left \{ {{x+(-y^{2})=6 } \atop {x*(-y^{2}) =-7}} \right. \\\\\left[\begin{array}{ccc}\left \{ {{x=7} \atop {-y^{2}=-1 }} \right. \\\left \{ {{x=-1} \atop {-y^{2} =7}}\right. \end{array}\right\\\\\\\left \{ {{x=7} \atop {-y^{2}=-1 }} \right.\\\\\left \{ {{x=7} \atop {y=\pm1}} \right. \\\\Otvet:\boxed{(7 \ ; \ -1) \ , \ (7 \ ; \ 1)}.$