Question Number 109699 by bemath last updated on 25/Aug/20
$$\:\:\:\:\:{x}\left({x}−\mathrm{1}\right)^{\mathrm{2}} \:\geqslant\:\mathrm{12}\left({x}−\mathrm{1}\right) \\ $$
Answered by bemath last updated on 25/Aug/20
$$\Leftrightarrow\:\left({x}−\mathrm{1}\right)\left({x}\left({x}−\mathrm{1}\right)−\mathrm{12}\right)\geqslant\mathrm{0} \\ $$$$\Leftrightarrow\left({x}−\mathrm{1}\right)\left({x}−\mathrm{4}\right)\left({x}+\mathrm{3}\right)\geqslant\mathrm{0} \\ $$$$\Leftrightarrow\:−\mathrm{3}\leqslant{x}\leqslant\mathrm{1}\:\cup\:{x}\geqslant\mathrm{4} \\ $$
Commented by nimnim last updated on 25/Aug/20
$$\mathrm{Nice}.. \\ $$