1) \(\sqrt[]{3x}-5\sqrt[]{12x}+7\sqrt[]{27x}=12\)
\(\Leftrightarrow\sqrt[]{3x}\left(1-5.2+7.3\right)=12\)
\(\Leftrightarrow\sqrt[]{3x}.12=12\)
\(\Leftrightarrow\sqrt[]{3x}=1\left(x\ge0\right)\)
\(\Leftrightarrow3x=1\)
\(\Leftrightarrow x=\dfrac{1}{3}\)
2) \(\sqrt[3]{x^2+2}=3\)
\(\Leftrightarrow\left(\sqrt[3]{x^2+2}\right)^3=3^3\)
\(\Leftrightarrow x^2+2=27\)
\(\Leftrightarrow x^2=25\)
\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-5\end{matrix}\right.\)
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