Решите систему уравнений {x^2+xy+y^2=75 {x^2-xy+y^2=25

Сначала найдем значение ху:
$\left \{ {{x^2+y^2=75-xy} \atop {x^2+y^2=25+xy}} \right. \\ 25+xy=75-xy\\ 2xy=75-25=50\\ xy=25$

$x^2+xy+y^2=75\\ +\\ x^2-xy+y^2=75\\ =\\ 2x^2+2y^2=100\\ \left \{ {{x^2+y^2=50} \atop {2xy=50}} \right. \\ x^2+y^2=2xy\\ x^2-2xy+y^2=0\\ (x-y)^=0\\ \left \{ {{x-y=0} \atop {xy=25}} \right. \\ \left \{ {{x=y} \atop {x^2=25}} \right. \\ x=y= \sqrt{25}=5 \\ x=y= \sqrt{25}=-5$