a) \(\sqrt[3]{x+3}=\sqrt[3]{x-9}\)
\(\Leftrightarrow x+3=x^2-9\)
\(\Leftrightarrow\left(x+3\right)\left(x-3\right)-\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\x-4=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=4\end{matrix}\right.\)
b) \(\sqrt[3]{x+2}-\sqrt{x+1}=1\)
\(\Leftrightarrow\sqrt[3]{x+2}=1+\sqrt{x+1}\left(x\ge-1\right)\)
\(\Leftrightarrow x+2=1+3\sqrt{x+1}+3\left(x+1\right)+\left(\sqrt{x+1}\right)^3\)
\(\Leftrightarrow\left(\sqrt{x+1}\right)^3+2\left(x+1\right)+3\sqrt{x+1}=0\)
\(\Leftrightarrow\sqrt{x+1}\left(x+1+2\sqrt{x+1}+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+1}=0\\\left(\sqrt{x+1}\right)^2+2\sqrt{x+1}+3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\\left(\sqrt{x+1}+1\right)^2+2=0\left(vô.lý\right)\end{matrix}\right.\)
\(\Leftrightarrow x=-1\left(tm\right)\)
