Câu 1:
\(\sqrt[3]{\left(3x+1\right)^2}+\sqrt[3]{\left(3x-1\right)^2}+\sqrt[3]{9x^2-1}=1\)
\(\Leftrightarrow\left(\sqrt[3]{3x+1}\right)^2+\left(\sqrt[3]{3x-1}\right)^2+\sqrt[3]{\left(3x-1\right)\left(3x+1\right)}=1\)
Đặt \(\left\{{}\begin{matrix}\sqrt[3]{3x+1}=a\\\sqrt[3]{3x-1}=m\end{matrix}\right.\), ta có hpt:
\(\left\{{}\begin{matrix}a^2+m^2+am=1\\a^3-m^3=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a^2+am+m^2=1\\\left(a-m\right)\left(a^2+am+m^2\right)=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a^2+am+m^2=1\left(1\right)\\a-m=2\left(2\right)\end{matrix}\right.\)
\(\left(2\right)\Rightarrow a=m+2\). Thay vào (1)
\(\Rightarrow\left(m+2\right)^2+\left(m+2\right)m+m^2=1\)
\(\Leftrightarrow3m^2+6m+3=0\)
\(\Leftrightarrow3\left(m+1\right)^2=0\)
\(\Leftrightarrow m=-1\)
\(\Rightarrow\sqrt[3]{3x-1}=-1\)
\(\Leftrightarrow3x-1=-1\)
\(\Leftrightarrow x=0\)
Câu 2: Đặt ẩn phụ và giải hpt như câu 1 >v<"
