Question

[Minh Anh]

Giải phương trình:

\(\sqrt[3]{x^2+3x+1}+x^2=\sqrt[3]{5x+1}+2x\)

Answer 1

[Nguyễn Việt Lâm]

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

\(\Rightarrow a+a^3-b^3=b\)

\(\Leftrightarrow a-b+\left(a-b\right)\left(a^2+ab+b^2\right)=0\)

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

\(\Leftrightarrow a=b\)

\(\Leftrightarrow\sqrt[3]{x^2+3x+1}=\sqrt[3]{5x+1}\)

\(\Leftrightarrow x^2+3x+1=5x+1\)

\(\Leftrightarrow...\)