Solve √(2x + 7) = x + 2. Enter the valid real solution for x.
Direct Answer: Extraneous Root Elimination is defined by: 1. Squaring gives 2x + 7 = x² + 4x + 4 => x² + 2x - 3 = 0 => (x + 3)(x - 1) = 0. x = -3 yields √1 = -1 (false). Only x = 1 is valid.
Detailed Step-by-Step Explanation:
Squaring gives 2x + 7 = x² + 4x + 4 => x² + 2x - 3 = 0 => (x + 3)(x - 1) = 0. x = -3 yields √1 = -1 (false). Only x = 1 is valid.