ĐKXĐ: ...
\(\Leftrightarrow x^3-\frac{1}{x^3}-3\left(x-\frac{1}{x}\right)-1=0\)
Đặt \(x-\frac{1}{x}=a\Rightarrow a^3=x^3-\frac{1}{x^3}-3\left(x-\frac{1}{x}\right)\)
\(\Rightarrow x^3-\frac{1}{x^3}=a^3+3\left(x-\frac{1}{x}\right)=a^3+3a\)
Phương trình trở thành:
\(a^3+3a-3a-1=0\Rightarrow a^3=1\Rightarrow a=1\)
\(\Rightarrow x-\frac{1}{x}=1\Rightarrow x^2-x-1=0\)