The correct option is D 0
|||x2−1|−1|+3|=1
⇒||x2−1|−1|+3=+1 or ||x2−1|−1|+3=−1
case −1, ||x2−1|−1|+3=+1
⇒||x2−1|−1|=−2,
That is not possible
case −2, ||x2−1|−1|+3=−1
⇒||x2−1|−1|=−4,
That is not possible
Hence, there is no solution for the given equation.
So, number of real solutions is 0
Alternate :
|||x2−1|−1|+3|=1
Since, we know that ||x2−1|−1|≥0 (always)
∴|||x2−1|−1|+3|≥3 (always)
∴|||x2−1|−1|+3|=1 has no real solution