\(\sqrt[3]{x+34}-\sqrt[3]{x-3}=1\)
Đặt \(\sqrt[3]{x+34}=a;\sqrt[3]{x-3}=b\)
Ta có \(\left\{{}\begin{matrix}a-b=1\\a^3-b^3=x+34-x+3=37\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a-b=1\\a^2+ab+b^2=37\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=b+1\\\left(b+1\right)^2+b\left(b+1\right)+b^2=37\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}a=4\\b=3\end{matrix}\right.\\\left\{{}\begin{matrix}a=-3\\b=-4\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}\sqrt[3]{x+34}=4\\\sqrt[3]{x-3}=3\end{matrix}\right.\\\left\{{}\begin{matrix}\sqrt[3]{x+34}=-3\\\sqrt[3]{x-3}=-4\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=30\\x=30\end{matrix}\right.\\\left\{{}\begin{matrix}x=-61\\x=-61\end{matrix}\right.\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=30\\x=-61\end{matrix}\right.\)
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