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Find the number of real solutions of the equation sin(pi*x) + x² + 1 = 2x.

1. 0
2. 1
3. 2
4. infinitely many

Correct answer: 1

Solution

The equation becomes sin(pi*x) = -(x-1)². At x = 1 both sides equal 0; for any other x the right side is strictly negative while equality forces a unique match, so there is exactly one solution.

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