Equations reducible to quadratics
Equations and inequalities · Mathematics
Study notes
Q: Solve x⁴ - 5x² + 4 = 0 and √(2x + 3) = x. Part A: Let y = x²: y² - 5y + 4 = 0 → (y - 1)(y - 4) = 0. y = 1 or 4. So x² = 1 or 4: x = ±1, ±2. Part B: Square: 2x + 3 = x² → x² - 2x - 3 = 0 → (x - 3)(x + 1) = 0. x = 3 or -1. Check: x = 3: √9 = 3 ✓. x = -1: √1 = 1 ≠ -1. Reject -1 (extraneous). Answer: x = 3.