Question

решите систему уравнений x^2+y^2=10 x+y=2

Answer 1

$\displaystyle \left \{ {{x^2+y^2=10} \atop {x+y=2}} \right. ~~\Rightarrow~~~\left \{ {{(x+y)^2-2xy=10} \atop {x+y=2}} \right. ~~~\Rightarrow~\left \{ {{4-2xy=10} \atop {x+y=2}} \right. \\ \Rightarrow~~~\left \{ {{-2xy=6} \atop {x+y=2}} \right. ~~~\Rightarrow~~~\left \{ {{(2-y)y=-3} \atop {x=2-y}} \right. \\ \\ -y^2+2y=-3\\ y^2-2y-3=0\\ (y-1)^2-4=0\\ (y-1-2)(y-1+2)=0\\ (y-3)(y+1)=0\\ y_1=3\\ y_2=-1\\ \\ x_1=2-y_1=2-3=-1\\ x_2=2-y_2=2+1=3$

Ответ: $(3;-1),~(-1;3).$

Answer 2

Решение во вложении.