Question

[Đoàn Nguyên Sa]

x³–x²–x=\(\frac{1_{ }}{3}\)

Answer 1

[Lê Minh Tú]

\(x^3-x^2-x=\frac{1}{3}\)

\(\Leftrightarrow x^3=x^2+x+\frac{1}{3}\)

\(\Leftrightarrow3x^2=3\left(x^2+x+\frac{1}{3}\right)\)

\(\Leftrightarrow3x^2=3x^2+3x+1\)

\(\Leftrightarrow3x^3+x^3=x^3+3x^3+3x+1\)

\(\Leftrightarrow4x^3=\left(x+1\right)^3\)

\(\Leftrightarrow\sqrt[3]{\left(4x^3\right)}=\sqrt[3]{\left(x+1\right)^3}\)

\(\Leftrightarrow\sqrt[3]{4.x}=x+1\)

\(\Leftrightarrow\sqrt[3]{4.x}-x=1\)

\(\Leftrightarrow x\left(\sqrt[3]{4}-1\right)=1\)

\(\Leftrightarrow x=\frac{1}{\left(\sqrt[3]{4}-1\right)}\)