If (x - 1)(x2 - 5x + 7) < (x - 1), then x belongs to

1) (1, 2) ∪ (3, ∞)

2) (- ∞, 1) ∪ (2, 3)

3) (2, 3)

4) None of the above

Solution: (2) (- ∞, 1) ∪ (2, 3)

(x – 1)(x2 – 5x + 7) < (x – 1)

∴ (x – 1) (x2 – 5x + 6) < 0

⇒ (x – 1) (x – 2) (x – 3) < 0

⇒ x ∈ (- ∞, 1) ∪ (2, 3)

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