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The point (a², a - 2) lies inside the region of the parabola y² = 2x that is bounded by the chord joining (2, 2) and (8, -4). How many integer values of a are possible?

1. 0
2. 1
3. 2
4. 3

Correct answer: 1

Solution

Imposing 'inside the parabola' and 'inside the chord' restricts a to a short interval containing exactly one integer.

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