For which values of x are the following statements true?
x2=−x
For this task you need the following basic knowledge: Square Roots
For which x do we have x2=−x?
In general, we have x2=|x|. So:
For which x is it true that |x|=−x?
Answer: For all values of x that are less than or equal to 0.
(x−1)2=x−1
This is true for all values x≥1 , since (x−1)2=|x−1| and the absolute value function is equal to the right-hand side exactly for x−1≥0 .