Find the value of x in the equation: √(3x + 1) – √(x + 4) = 1

Move one root across: √(3x + 1) = 1 + √(x + 4). Square both sides: 3x + 1 = 1 + 2√(x + 4) + x + 4.

Simplify: 2x – 4 = 2√(x + 4), so x – 2 = √(x + 4). Square again: x² – 4x + 4 = x + 4, so x² – 5x = 0. This gives x = 0 or x = 5.

Check both, because squaring can add false answers. x = 0: √1 – √4 = -1, not 1. x = 5: √16 – √9 = 4 – 3 = 1. So x = 5.