Question

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

Answer 1

Đặt \(\sqrt[3]{2+x}=a\) ; \(\sqrt[3]{2-x}=b\) . Ta có hệ phương trình :

\(\left\{{}\begin{matrix}a+b=4\\a^3+b^3=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a^2+2ab+b^2=16\\a^2-ab+b^2=\dfrac{1}{4}\end{matrix}\right.\Leftrightarrow3ab=\dfrac{63}{4}\Leftrightarrow ab=\dfrac{21}{4}\)

\(\Rightarrow\left\{{}\begin{matrix}a+b=4\\ab=\dfrac{21}{4}\end{matrix}\right.\Leftrightarrow a^2-4a+\dfrac{21}{4}=0\Leftrightarrow a\in\varnothing\) . Vậy pt vô nghiệm