Question

Giải bpt :

\(\sqrt[3]{2x+1}+\sqrt[3]{x}=1\)

Answer 1

Đặt \(\left\{{}\begin{matrix}\sqrt[3]{2x+1}=a\\\sqrt[3]{x}=b\end{matrix}\right.\) ta được hệ:

\(\left\{{}\begin{matrix}a+b=1\\a^3-2b^3=1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}a=1-b\\a^3-2b^3=1\end{matrix}\right.\)

\(\Rightarrow\left(1-b\right)^3-2b^3=1\)

\(\Leftrightarrow1-3b+3b^2-b^3-2b^3=1\)

\(\Leftrightarrow-3b\left(b^2-b+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}b=0\\b^2-b+1=0\left(vn\right)\end{matrix}\right.\) \(\Rightarrow\sqrt[3]{x}=0\Rightarrow x=0\)