Question

Find all real solutions to the equation with absolute value
$|x-1|=|x^2-2x+1|$

• A. no solutions
• B. $0$
• C. $3$
• D. $0,1,2$
• E. $2+\sqrt{2},2-\sqrt{2}$

Answer 1

The correct option is D $0,1,2$

$|x-1|=|x^2-2x+1|x-1=\pm (x^2-2x+1)$

$x-1=x^2-2x+1$ or $x-1=-(x^2-2x+1)$

$x^2-3x+2=0$ or $x-1={-x}^2+2x-1$

$x=1,2$ or $x^2-x=0$

$x=0,1$

$x=0,1,2$