Question

Решить уравнение: |x-1| = |x^2-3x+2|

Answer 1

$|x-1|=|x^2-3x+2|\\|x-1|=|x-1|\cdot |x-2|\\|x-1|(1-|x-2|)=0\\\left[ \begin{gathered} |x-1|=0 \\ |x-2|=1 \\ \end{gathered} \right.\Rightarrow \left[ \begin{gathered} x=1 \\ x=\left \{ 1;3 \right \} \\ \end{gathered} \right.\Rightarrow x=\left \{ 1;3 \right \}$