ISI 2015 PCB A2

Question

Find all real solutions of the equation $x^{2} - |x-1| - 3 = 0$

Answer 1

$x = 1$ does not satisfy the equation

considering the domain $x > 1$

$x^{2}-(x-1)-3=0\\ x^{2}-x-2=0$

$x=2$

considering the domain $x<1$

$x^{2}-(1-x)-3=0\\ x^{2}+x-4=0$

$x=\frac{-1-\sqrt{17}}{2}$