Система уравнений! Помогите!
x^2-xy+y^2=19
x^2+xy+y^2=49

$left { {{x^2-xy+y^2=19 } atop {x^2+xy+y^2=49 }} right.$
$left { {{ x^{2} + y^{2} =19 + xy} atop {x^{2} + y^{2} = 49 - xy}} right. 19+xy=49-xy 2xy=30 xy=15 left { {{ x^{2} + y^{2} =19 + 15} atop {x^{2} + y^{2} = 49 - 15}} right. left { {{ x^{2} + y^{2} = 34} atop {x^{2} + y^{2} = 34}} right.$
Дальше формула $x^{2} + y^{2} = x^{2} +2xy+ y^{2} -2xy= (x+y)^{2} -2xy$
$(x+y)^{2} -2xy=34 (x+y)^{2} -2*15=34 (x+y)^{2} =64 x+y=8$
Затем находим сами корни:
$left { {{y=8-x} atop { x^{2} +x(8-x)+(8-x)^2=49}} right. x^{2} +8x-x^2+64-x^2=49 x^2-8x+15=0 D=64-60=4 left { {{x_{1} = frac{8+2}{2}=5 } atop {x_{2} = frac{8-2}{2}=3 }} right. left[begin{array}{ccc} left { {{x_{1}=5} atop { y_{1} =8-x_{1}=8-5=3}} right. left { {{x_{2}=3} atop { y_{2} =8-x_{2}=8-3=5}} right.end{array}right$

Ответ: $left { {{ x_{1}=3 } atop { y_{1}=5 }} right.$ или $left { {{ x_{2}=5 } atop { y_{2} =3}} right.$