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Problem 14 - Entrance Test

Solve for x: sqrt(x + 2) + sqrt(x + 5) = 3

Correct: A

sqrt(x+5) = 3 - sqrt(x+2). Squaring both sides: x+5 = 9 - 6sqrt(x+2) + x + 2. Simplifying: 6sqrt(x+2) = 6. sqrt(x+2) = 1. Squaring both sides: x+2 = 1. So, x = -1. Checking the solution: sqrt(-1+2) + sqrt(-1+5) = sqrt(1) + sqrt(4) = 1 + 2 = 3. Therefore, x = -1.