VietaTheorem
Intermediate
Let real numbers $a$, $b$, and $c$ satisfy
$$
\left\{
\begin{array}{rcl}
a^2 - bc-8a +7&=&0\\
b^2 + c^2 +bc-6a+6&=&0
\end{array}
\right.
$$
Show that $1 \le a \le 9$.
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