Question

Giải PT: \(\sqrt[3]{2x+4}=\sqrt[3]{2x-1}+\sqrt[3]{5}\)

Answer 1

Đặt \(\left\{{}\begin{matrix}2x-1=a\\5=b\end{matrix}\right.\),\(Pt\Leftrightarrow\sqrt[3]{a+b}=\sqrt[3]{a}+\sqrt[3]{b}\)

\(\Leftrightarrow a+b=a+b+3\sqrt[3]{ab}\left(\sqrt[3]{a}+\sqrt[3]{b}\right)\)

\(\Leftrightarrow\sqrt[3]{ab}\left(\sqrt[3]{a}+\sqrt[3]{b}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}a=0\\b=0\\a=-b\end{matrix}\right.\)

*: \(a=0\Leftrightarrow x=\dfrac{1}{2}\)

*:b=0: vô lý

*:\(a=-b\Leftrightarrow2x-1=-5\Leftrightarrow x=-2\)