Ta có: \(\left(x-2\right)^3+\left(3x-1\right)\left(3x+1\right)=\left(x+1\right)^3\)
\(\Leftrightarrow x^3-6x^2+12x-8+9x^2-1=x^3+3x^2+3x+1\)
\(\Leftrightarrow x^3+3x^2+12x-9-x^3-3x^2-3x-1=0\)
\(\Leftrightarrow9x-10=0\)
\(\Leftrightarrow9x=10\)
hay \(x=\frac{10}{9}\)
Vậy: \(x=\frac{10}{9}\)