Question 158
Find all solutions, in the set of positive real numbers, of the system of equations:
$$
\left\{\begin{array}{l}
x(x+y+z)=26 \\
y(x+y+z)=27 \\
z(x+y+z)=28
\end{array}\right.
$$
$$
\left\{\begin{array}{l}
x(x+y+z)=26 \\
y(x+y+z)=27 \\
z(x+y+z)=28
\end{array}\right.
$$