Question

Решить уравнение

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

Answer 1

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

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

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

$xin(-sqrt{5}; -sqrt{2})cup(sqrt{5}; +infty)$