Đáp án:
24
Giải thích các bước giải:
$\begin{array}{l}
P = \frac{{4x}}{{\sqrt x - 3}} = \frac{{4x - 36}}{{\sqrt x - 3}} + \frac{{36}}{{\sqrt x - 3}}\\
= 4\left( {\sqrt x + 3} \right) + \frac{{36}}{{\sqrt x - 3}} = 4\left( {\sqrt x - 3} \right) + \frac{{36}}{{\sqrt x - 3}} + 24\\
\ge 2\sqrt {4\left( {\sqrt x - 3} \right).\frac{{36}}{{\sqrt x - 3}}} + 24\\
= 2.\sqrt {4.36} + 24 = 48\\
\Rightarrow {P_{\min }} = 48\,khi\,4\left( {\sqrt x - 3} \right) = \frac{{36}}{{\sqrt x - 3}}\\
\Leftrightarrow {\left( {\sqrt x - 3} \right)^2} = 3 \Leftrightarrow \sqrt x - 3 = \pm \sqrt 3 \\
\Leftrightarrow \left[ \begin{array}{l}
\sqrt x = 3 + \sqrt 3 \\
\sqrt x = 3 - \sqrt 3
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = {\left( {3 + \sqrt 3 } \right)^2}\\
x = {\left( {3 - \sqrt 3 } \right)^2}
\end{array} \right.
\end{array}$
