Problem: For how many real numbers x is β(x+1)2β a real number?
Answer Choices:
A. none
B. two
C. infinitely many
D. one
E. a finite number greater than two
Solution:
If x+1ξ =0 then β(x+1)2<0 and β(x+1)2β is not real; if x+1=0 then ββ(xΛ+1)2=0. Thus x=β1 is the only value of x for which the given ex pression is real.