Question

If $\{x\in R|x^2=|x-2|\}$, then $x$ is equal to

• A. $\{-1,2\}$
• B. $\{1,2\}$
• C. $\{-1,-2\}$
• D. $\{1,-2\}$

Answer 1

The correct option is D $\{1,-2\}$

The equation can be written as $x-2=x^2$ for $x>2$
$x^2-x+2=0$
As $b^2-4ac<0$, the equation always gives positive value and never touches $x$ axis so has imaginary roots.
Now, lets consider the case when $x<2$ then the equation becomes $2-x=x^2$.
$x^2+x-2$=$(x-1)(x+2)$
$x=-2,1$
Hence, correct answer is option D.