Đáp án:
\(x = \frac{{144}}{{25}}\)
Giải thích các bước giải:
\(\begin{array}{l}
- 5x + 7\sqrt x + 12 = 0\\
DK:\,\,\,x \ge 0\\
pt \Leftrightarrow - 5x - 5\sqrt x + 12\sqrt x + 12 = 0\\
\Leftrightarrow - 5\sqrt x \left( {\sqrt x + 1} \right) + 12\left( {\sqrt x + 1} \right) = 0\\
\Leftrightarrow \left( {\sqrt x + 1} \right)\left( {12 - 5\sqrt x } \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sqrt x + 1 = 0\\
12 - 5\sqrt x = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\sqrt x = - 1\,\,\left( {VN} \right)\\
5\sqrt x = 12
\end{array} \right.\\
\Leftrightarrow \sqrt x = \frac{{12}}{5} \Leftrightarrow x = \frac{{144}}{{25}}\,\,\,\,\left( {tm} \right).\\
Vay\,\,\,x = \frac{{144}}{{25}}.
\end{array}\)