Question

Решить уравнение

$|x^4-x^3+x^2+5x-6|\ \textless \ x^4+x^3+x^2-5x-6$

Answer 1

$|T|\ \textless \ U\ \ \ \ \ \textless \ -\ \textgreater \ \ \ \ \ -U\ \textless \ T\ \textless \ U$

$|x^4-x^3+x^2+5x-6|\ \textless \ x^4+x^3+x^2-5x-6\\\\ \begin{equation*} \begin{cases} x^4-x^3+x^2+5x-6\ \textless \ x^4+x^3+x^2-5x-6 \\ -x^4-x^3-x^2+5x+6\ \textless \ x^4-x^3+x^2+5x-6 \end{cases} \end{equation*} \\\\ \begin{equation*} \begin{cases} -x^3+5x\ \textless \ x^3-5x \\ -x^4-x^2+6\ \textless \ x^4+x^2-6 \end{cases} \end{equation*} \\ \begin{equation*} \begin{cases} x^3-5x\ \textgreater \ 0 \\ x^4+x^2-6\ \textgreater \ 0 \end{cases} \end{equation*} \\ \begin{equation*} \begin{cases} x(x-\sqrt{5})(x+\sqrt{5})\ \textgreater \ 0 \\ (x^2+3)(x^2-2)\ \textgreater \ 0 \end{cases} \end{equation*}$

$\\ \begin{equation*} \begin{cases} x(x-\sqrt{5})(x+\sqrt{5})\ \textgreater \ 0 \\ (x^2+3)(x^2-2)\ \textgreater \ 0 \end{cases} \end{equation*} \\ \begin{equation*} \begin{cases} x\in(-\sqrt{5};\ 0)\cup(\sqrt{5};\ +\infty) \\ x\in(-\infty;\ -\sqrt{2})\cup(\sqrt{2};+\infty) \end{cases} \end{equation*}$

$x\in(-\sqrt{5};\ -\sqrt{2})\cup(\sqrt{5};\ +\infty)$