Đáp án:
\(\left[ \begin{array}{l}
x = 1,389193597\\
x = - 2
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
(x - 1) - \left| {{x^2} + 2x - 6} \right| = {x^3} - 1\\
\to \left| {{x^2} + 2x - 6} \right| = x - 1 - {x^3} + 1\\
\to \left[ \begin{array}{l}
{x^2} + 2x - 6 = x - {x^3}\\
{x^2} + 2x - 6 = - x + {x^3}
\end{array} \right.\\
\to \left[ \begin{array}{l}
{x^3} + {x^2} + x - 6 = 0\\
{x^3} - {x^2} - 3x + 6 = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
{x^3} + {x^2} + x - 6 = 0\\
{x^3} + 2{x^2} - 3{x^2} - 6x + 3x + 6 = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 1,389193597\\
{x^2}\left( {x + 2} \right) - 3x\left( {x + 2} \right) + 3\left( {x + 2} \right) = 0
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 1,389193597\\
x + 2 = 0\\
{x^2} - 3x + 3 = 0\left( {vô lý} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 1,389193597\\
x = - 2
\end{array} \right.
\end{array}\)
