Question 144
Let $a\gt 0$. If the system
$$
\left\{\begin{array}{l}
a^{x}+a^{y}+a^{z}=14-a \\
x+y+z=1
\end{array}\right.
$$
has a solution in real numbers, prove that $a \leq 8$.
$$
\left\{\begin{array}{l}
a^{x}+a^{y}+a^{z}=14-a \\
x+y+z=1
\end{array}\right.
$$
has a solution in real numbers, prove that $a \leq 8$.