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Question Number 148515 by mathdanisur last updated on 28/Jul/21

Find the sum of the roots of the equation:  x^2  - 2x - 3 ∣x - 1∣ + 3 = 0

$${Find}\:{the}\:{sum}\:{of}\:{the}\:{roots}\:{of}\:{the}\:{equation}: \\ $$$${x}^{\mathrm{2}} \:-\:\mathrm{2}{x}\:-\:\mathrm{3}\:\mid{x}\:-\:\mathrm{1}\mid\:+\:\mathrm{3}\:=\:\mathrm{0} \\ $$

Answered by dumitrel last updated on 28/Jul/21

∣x−1∣^2 −3∣x−1∣+2=0⇒∣x−1∣∈{1,2}  x−1∈{±1;±2}⇒sum=4

$$\mid{x}−\mathrm{1}\mid^{\mathrm{2}} −\mathrm{3}\mid{x}−\mathrm{1}\mid+\mathrm{2}=\mathrm{0}\Rightarrow\mid{x}−\mathrm{1}\mid\in\left\{\mathrm{1},\mathrm{2}\right\} \\ $$$${x}−\mathrm{1}\in\left\{\pm\mathrm{1};\pm\mathrm{2}\right\}\Rightarrow{sum}=\mathrm{4} \\ $$

Commented by mathdanisur last updated on 28/Jul/21

Thank you Ser cool

$${Thank}\:{you}\:{Ser}\:{cool} \\ $$

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