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Solve the equation sqrt(2x + 1) = sqrt(x) + 1 for x.

1. x = 0 or x = 4
2. x = 4 only
3. x = 1 only
4. no real solution

Correct answer: x = 0 or x = 4

Solution

Square: 2x + 1 = x + 2sqrt(x) + 1 ⇒ x = 2sqrt(x) ⇒ x - 2sqrt(x) = 0 ⇒ sqrt(x)(sqrt(x) - 2) = 0 ⇒ sqrt(x) = 0 or 2 ⇒ x = 0 or x = 4. Both satisfy the original (x=0: sqrt(1)=1=0+1 ✓; x=4: sqrt(9)=3=2+1 ✓).

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