My approach was a hybrid:
I) & II) were straightforward FALSE/TRUE. -> Option D was ruled out
III) Didn't even made any calculation since was present in all the remaining answers
IV) Did the math
a=b^2 ; x-1 = (x+2)^2 ; x^2+3x+5=0 ; since I couldn't find any "integer" solution I flagged it FALSE
V) Did the math
b=a^2 ; x+2 = (x-1)^2 ; x^2-3x+1=0; since I couldn't find any "integer" solution I flagged it FALSE
Wrongly, I selected choice E
Making the assumption of the integer solution I didn't think of any other real number as roots of the equations on IV and V.
Thanks for this good question
stonecold, even knowing that real numbers could be a possible solution, I wouldn't figure out to use the Discriminant of a Quadratic to help me out.