Đáp án:
$\begin{array}{l}
x\left( {x + 5} \right) = 3\sqrt[3]{{{x^2} + 5x + 2}} - 4\\
\Rightarrow {x^2} + 5x + 2 = 3\sqrt[3]{{{x^2} + 5x + 2}} + 2 - 4\\
\Rightarrow {\left( {\sqrt[3]{{{x^2} + 5x + 2}}} \right)^3} - 3\sqrt[3]{{{x^2} + 5x + 2}} + 2 = 0\\
Dat:\sqrt[3]{{{x^2} + 5x + 2}} = a\\
\Rightarrow {a^3} - 3a + 2 = 0\\
\Rightarrow {a^3} - {a^2} + {a^2} - a - 2a + 2 = 0\\
\Rightarrow \left( {a - 1} \right)\left( {{a^2} + a - 2} \right) = 0\\
\Rightarrow \left( {a - 1} \right)\left( {a - 1} \right)\left( {a + 2} \right) = 0\\
\Rightarrow {\left( {a - 1} \right)^2}\left( {a + 2} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
a = 1\\
a = - 2
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
\sqrt[3]{{{x^2} + 5x + 2}} = 1\\
\sqrt[3]{{{x^2} + 5x + 2}} = - 2
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
{x^2} + 5x + 2 = 1\\
{x^2} + 5x + 2 = - 8
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
{x^2} + 5x + 1 = 0\\
{x^2} + 5x + 10 = 0\left( {vo\,nghiem} \right)
\end{array} \right.\\
\Rightarrow {x^2} + 2.5x + \dfrac{{25}}{4} - \dfrac{{21}}{4} = 0\\
\Rightarrow {\left( {x + \dfrac{5}{2}} \right)^2} = \dfrac{{21}}{4}\\
\Rightarrow x = \dfrac{{ - 5 \pm \sqrt {21} }}{4}
\end{array}$
