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Problem 19 - Entrance Test

The number of real solutions of √(x+2) + √(x-3) = 5 is

Correct: B

Domain x ≥ 3. Isolate one root and square: √(x+2) = 5 - √(x-3) → x+2 = 25 - 10√(x-3) + x-3 → 10√(x-3) = 20 → √(x-3) = 2 → x = 7. Check: √9 + √4 = 3 + 2 = 5. Only one solution.