Đáp án:
\(\left[ \begin{array}{l}
x = - 3\\
x = - 10
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\sqrt[3]{{x + 11}} = 3 + \sqrt[3]{{x + 2}}\\
\to x + 11 = 27 + 3.9.\sqrt[3]{{x + 2}} + 3.3.\sqrt[3]{{{{\left( {x + 2} \right)}^2}}} + x + 2\\
\to 16 + 27\sqrt[3]{{x + 2}} + 9\sqrt[3]{{{{\left( {x + 2} \right)}^2}}} + 2 = 0\\
\to 9\sqrt[3]{{{{\left( {x + 2} \right)}^2}}} + 27\sqrt[3]{{x + 2}} + 18 = 0\\
\to \sqrt[3]{{{{\left( {x + 2} \right)}^2}}} + 3\sqrt[3]{{x + 2}} + 2 = 0\\
\to \left( {\sqrt[3]{{x + 2}} + 1} \right)\left( {\sqrt[3]{{x + 2}} + 2} \right) = 0\\
\to \left[ \begin{array}{l}
\sqrt[3]{{x + 2}} + 1 = 0\\
\sqrt[3]{{x + 2}} + 2 = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
\sqrt[3]{{x + 2}} = - 1\\
\sqrt[3]{{x + 2}} = - 2
\end{array} \right.\\
\to \left[ \begin{array}{l}
x + 2 = - 1\\
x + 2 = - 8
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = - 3\\
x = - 10
\end{array} \right.
\end{array}\)
