Problem: For how many real numbers x is −(x+1)2​ a real number?
Answer Choices:
A. none
B. two
C. infinitely many
D. one
E. a finite number greater than two
Solution:
If x+1î€ =0 then −(x+1)2<0 and −(x+1)2​ is not real; if x+1=0 then ​−(xˉ+1)2=0. Thus x=−1 is the only value of x for which the given ex pression is real.