Question

Answer 1

\(3x-1=\sqrt[3]{\dfrac{12+\sqrt{135}}{3}}+\sqrt[3]{\dfrac{12-\sqrt{135}}{3}}\)

\(\Leftrightarrow\left(3x-1\right)^3=\left(\sqrt[3]{\dfrac{12+\sqrt{135}}{3}}+\sqrt[3]{\dfrac{12-\sqrt{135}}{3}}\right)^3\)

\(\Leftrightarrow27x^3-27x^2+9x-1=8+3\left(3x-1\right)\)

\(\Leftrightarrow27x^3-27x^2-9=-3\)

\(\Leftrightarrow9x^3-9x^2-3=-1\)