The number of the real solutions of the equation: $x|x+3|+|x-1|-2=0$ is
(1) 2
(2) 4
(3) 3
(4) 5
Step-by-Step Solution
Key Concept: Critical points at $x=-3$ and $x=1$. Analyse the equation case-by-case in the three regions $(-\infty,-3)$, $[-3,1)$, and $[1,\infty)$.
3 real solutions: $x=-2-\sqrt{3},\,-1-\sqrt{2},\,-1+\sqrt{2}$.
Correct Answer: 3