Đáp án:
$\begin{array}{l}
P = \dfrac{{2x}}{{{x^2} - 2x + 4}}\\
\Rightarrow P.{x^2} - 2P.x + 4P = 2x\\
\Rightarrow P.{x^2} - 2.\left( {P + 1} \right).x + 4P = 0\left( * \right)
\end{array}$
Để pt (*) có nghiệm x thì:
$\begin{array}{l}
+ Khi:P = 0\\
\Rightarrow - 2x = 0\\
\Rightarrow x = 0\left( {tmdk} \right)\\
+ Khi:P \ne 0\\
\Rightarrow \Delta ' \ge 0\\
\Rightarrow {\left( {P + 1} \right)^2} - 4{P^2} \ge 0\\
\Rightarrow {P^2} + 2P + 1 - 4{P^2} \ge 0\\
\Rightarrow 3{P^2} - 2P - 1 \le 0\\
\Rightarrow \left( {3P + 1} \right)\left( {P - 1} \right) \le 0\\
\Rightarrow - \dfrac{1}{3} \le P \le 1\\
\Rightarrow \left\{ \begin{array}{l}
GTNN:P = - \dfrac{1}{3}\,Khi:x = - 2\\
GTLN:P = 1\,khi:x = 2
\end{array} \right.
\end{array}$
