Problem

Source: 2010 Saudi Arabia BMO TST 4.4 - Balkan Math Olympiad

Tags: system of equations, System, algebra



Let $a > 0$. If the system $$\begin{cases} a^x + a^y + a^z = 14 - a \\ x + y + z = 1 \end{cases}$$has a solution in real numbers, prove that $a \le 8$.