Question

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

Answer 1

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

\(a+b=1+ab\) \(a-1-b\left(a-1\right)=0\) \(\Rightarrow\left(a-1\right)\left(1-b\right)=0\)

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

Answer 2

Chỗ \(a+b=1+ab\Rightarrow a-1-b\left(a-1\right)=0\) ghi thiếu dấu suy ra hay tương đương gì đó