Question Number 207487 by hardmath last updated on 17/May/24
$$\mid\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{3x}\:−\:\mathrm{4}\mid\:=\:\mid\mathrm{x}\:−\:\mathrm{4}\mid \\ $$$$\mathrm{find}:\:\:\:\boldsymbol{\mathrm{min}}\:\:\mathrm{and}\:\:\boldsymbol{\mathrm{max}}\:\:=\:\:? \\ $$
Answered by A5T last updated on 17/May/24
$$\mid{x}−\mathrm{4}\mid\mid{x}+\mathrm{1}\mid=\mid{x}−\mathrm{4}\mid\Rightarrow\mid{x}−\mathrm{4}\mid=\mathrm{0}\:{or}\:\mid{x}+\mathrm{1}\mid=\mathrm{1} \\ $$$$\Rightarrow{x}−\mathrm{4}=\mathrm{0}\:{or}\:{x}+\mathrm{1}=\mathrm{1}\:{or}\:{x}+\mathrm{1}=−\mathrm{1} \\ $$$$\Rightarrow{x}=\mathrm{4}\:{or}\:\mathrm{0}\:{or}\:−\mathrm{2}\Rightarrow\:{min}=−\mathrm{2};\:{max}=\mathrm{4} \\ $$
Commented by hardmath last updated on 17/May/24
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{professor} \\ $$