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Let S = {x ∈ R: x ≥ 0 and 2|√x − 3| + √x(√x − 6) + 6 = 0}. Then S:

1. contains exactly one element.
2. contains exactly two elements.
3. contains exactly four elements.
4. is an empty set.

Correct answer: contains exactly two elements.

Solution

The equation simplifies to a quadratic form that can be analyzed for its roots. Upon solving, it reveals two valid solutions for x that satisfy the conditions of the set S, confirming that it contains exactly two elements.

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