Question

Пожалуйста, решите систему

Answer 1

$\left\{\begin{matrix}xy+z+y=80\left ( 1 \right )\\ yz+y+z=80\left ( 2 \right )\\ zx+z+x=80\left ( 3 \right )\end{matrix}\right.\\\left ( 1 \right )-\left ( 2 \right )=-z\left ( y+1 \right )+xy+z=0\\\left ( y+1 \right )\left ( x-z \right )=0\\y=-1\Rightarrow -81\neq 0$

$x=z\Rightarrow \left\{\begin{matrix}yz+y+z=80\\ z^2+2z=80\end{matrix}\right.\Leftrightarrow \left\{\begin{matrix}yz+y+z=80\\ z=\left \{ -10;8 \right \}\end{matrix}\right.\\z=-10\Rightarrow \left ( x;y \right )=\left ( -10;-10 \right )\\z=8\Rightarrow \left ( x;y \right )=\left ( 8;8 \right )$