Question

Решите систему неравенств
$\left \{ {{x^{2} -x\geq0 } \atop {IxI<2}} \right.$

Answer 1

$\left \{ {{x^2-x\geq0 } \atop {|x|<2}} \right. =>\left \{ {{x(x-1)\geq0 } \atop {|x|<2}} \right. =>\left \{ {{x\leq0;x\geq1  } \atop {-2<x<2}} \right. =>-2<x\leq 0;1\leq x<2$

Answer 2

$\left \{ {{x^2-x\geq 0} \atop {|x|<2}} \right.\; \; \left \{ {{x(x-1)\geq 0} \atop {-2<x<2}} \right.\; \; \left \{ {{x\in (-\infty ,0\, ]\, \cup \, [\, 1,+\infty )} \atop {x\in (-2,2)}} \right.\; \; \Rightarrow \; \; x\in (-2,0\, ]\cup [\, 1,2)$