# The equation [ x – 1][x + 1] = a^2 – 2a – 3 can have real solutions for x if a belongs to ( – infinity to – 1] union [ 3 to infinity) [ 1 – underroot 5 , – ] union [3, 1+ underroot 5] [1 – underroot 5, 1+underroot 5]

Arun Kumar IIT Delhi
8 years ago
Hello Student,
By what i understand by your representation.
$(x^2-1) = a^2-2a-3 \\=>a^2-2a-2 \geq 0 \\=>(a-1)^2-3 \geq 0 \\=>(a-1) \in (-\infty,\sqrt3] \bigcup [\sqrt3,\infty]$
Thanks & Regards
Arun Kumar
Btech, IIT Delhi