Quadratic Equations and Inequalities: Modulus equation MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

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Modulus equationMediumQuestion 220022

Question

The number of real solutions of |x² − 1| = x is:

A
0
B
1
C
2
Correct
D
3

Correct answer

Explanation

Case 1: x²−1 = x (x ≥ 0 region where x²≥1): x²−x−1=0, x=(1+√5)/2 (valid). Case 2: 1−x² = x → x²+x−1=0, x=(−1+√5)/2 (positive, valid since x²<1 here). Total: 2 solutions.

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