Question

Система рiвняннь Срочно!

Answer 1

$\left\{\begin{array}{ccc}x^{2}+y^{2}+xy=7\\x+y+xy=5\end{array}\right\\\\\\\left\{\begin{array}{ccc}(x+y)^{2}-2xy+xy=7 \\x+y+xy=5\end{array}\right\\\\\\\left\{\begin{array}{ccc}(x+y)^{2}-xy=7 \\(x+y)+xy=5\end{array}\right\\\\x+y=m \ , \ xy=n\\\\+\left\{\begin{array}{ccc}m^{2}-n=7 \\m+n=5\end{array}\right \\---------\\m^{2}+m=12\\\\m^{2}+m-12=0\\\\m_{1} =-4\\\\m_{2}=3-teorema \ Vieta\\\\n_{1} =5-(-4)=5+4=9\\\\n_{2}=5-3=2$

$1)\\\left\{\begin{array}{ccc}x+y=-4\\xy=9\end{array}\right\\\\\\\left\{\begin{array}{ccc}x=-4-y\\(-4-y)\cdot y=9\end{array}\right\\\\\\\left\{\begin{array}{ccc}x=-4-y\\y^{2}+4y+9=0 \end{array}\right \\\\y^{2}+4y+9=0\\\\D=4^{2}-4\cdot 9=16-36=-20<0\\\\y\in\oslash\\\\\\2)\\\left\{\begin{array}{ccc}x+y=3\\xy=2\end{array}\right \\\\\\\left\{\begin{array}{ccc}x=3-y\\(3-y)\cdot y=2\end{array}\right\\\\\\\left\{\begin{array}{ccc}x=3-y\\y^{2} -3y+2=0\end{array}\right$

$y^{2}-3y+2=0\\\\y_{1}=1\\\\y_{2}=2\\\\x_{1} =3-1=2\\\\x_{2}=3-2=1\\\\Otvet:\boxed{(1 \ ; \ 2) \ , \ (2 \ ; \ 1)}$