Question Number 148515 by mathdanisur last updated on 28/Jul/21
$${Find}\:{the}\:{sum}\:{of}\:{the}\:{roots}\:{of}\:{the}\:{equation}: \\ $$$${x}^{\mathrm{2}} \:-\:\mathrm{2}{x}\:-\:\mathrm{3}\:\mid{x}\:-\:\mathrm{1}\mid\:+\:\mathrm{3}\:=\:\mathrm{0} \\ $$
Answered by dumitrel last updated on 28/Jul/21
$$\mid{x}−\mathrm{1}\mid^{\mathrm{2}} −\mathrm{3}\mid{x}−\mathrm{1}\mid+\mathrm{2}=\mathrm{0}\Rightarrow\mid{x}−\mathrm{1}\mid\in\left\{\mathrm{1},\mathrm{2}\right\} \\ $$$${x}−\mathrm{1}\in\left\{\pm\mathrm{1};\pm\mathrm{2}\right\}\Rightarrow{sum}=\mathrm{4} \\ $$
Commented by mathdanisur last updated on 28/Jul/21
$${Thank}\:{you}\:{Ser}\:{cool} \\ $$