If 1 < x < 2, then the value of √(x − 1)2 +

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If 1 < x < 2, then the value of √(x − 1)² + √(x − 3)² is

1. 1
2. 2
3. 3
4. 2x–4

Correct Option: B

Since 1 < x < 2, we have
x – 1 > 0 and
x – 3 < 0
or, 3 – x > 0
∴ √(x − 1)² + √(x − 3)²
= √(x − 1)² + √(3 − x)²
[∴ (x − 3)² = (3 – x)²]
= x – 1 + 3 – x = 2