Question Number 178640 by CrispyXYZ last updated on 19/Oct/22
$$\forall−\mathrm{1}\leqslant{a}\leqslant\mathrm{1},\:\exists\mathrm{0}\leqslant{b}\leqslant\mathrm{2},\:{x}^{\mathrm{2}} −\mathrm{2}{ax}+{a}\geqslant\mid{b}−\mathrm{1}\mid+\mid{b}−\mathrm{2}\mid \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{x}.\:\left({x}\in\mathbb{R}\right) \\ $$