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Algebra
Inequalities, Absolute Value Inequalities
jee_adv_2026_mock_p2
Grade 12

Question:

The number of integral values of x satisfying |x^2 - 4x + 3| < 2 is:

Step-by-Step Solution

Key Concept: Solve the inequality by considering the quadratic expression.
Step 1: x^2 - 4x + 3 = (x-1)(x-3). Step 2: Let y = x - 2. Then (x-1)(x-3) = y^2 - 1. Step 3: |y^2 - 1| < 2 => -2 < y^2 - 1 < 2 => -1 < y^2 < 3 => y^2 < 3 => |y| < √3. Step 4: x ∈ (2-√3, 2+√3) ≈ (0.268, 3.732). Step 5: Integral values: 1, 2, 3. That's 3 values.
Correct Answer: 3
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