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Find the number of solutions of the equation cot⁻¹(sqrt(4 - x²)) + cos⁻¹(x² - 5) = 3*pi/2.

1. 2
2. 4
3. 6
4. 8

Correct answer: 2

Solution

Both inverse functions must hit their maximum compatible values simultaneously. The domain constraints from sqrt(4 - x²) and cos⁻¹(x² - 5) pin x to specific values, giving a finite count of solutions.

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