Розділ 3. КВАДРАТНІ РІВНЯННЯ » 21.13

Розв’яжіть рівняння: 1) (x + 2)2 = 2x + 3; x² + 4x + 4 – 2х – 3 = 0; x² + 2x + 1 = 0; D = 2² – 4 • 1 • 1 = 0; х = (-2)/2 = –1. 2) 5(x – 2)² = 3х – 6; 5(x² – 4x + 4) – 3х + 6 = 0; 5x² – 20x + 20 – 3х + 6 = 0; 5x² – 23x + 26 = 0; D = (–23)² – 4 • 5 • 26 = 9; √D = 3; х1 = (23+3)/(2•5) = 26/10 = 2,6; х2 = (23-3)/10 = 2. 3) (x + 2)(x – 3) = 2x(x – 4) + 6; x² – 3х + 2x – 6 = 2x² – 8х + 6; 2x² – 8х + 6 – x² + x + 6 = 0; x² – 7x + 12 = 0; D = (–7)² – 4 • 1 • 12 = 1; √D = 1; х1 = (7+1)/2 = 4; х2 = (7-1)/2 = 3. 4) х(х – 1) – (x – 3)(x + 3) = (x + 2)² – 1; x² – x – (x² – 9) = x² + 4x + 4 – 1; x² + 4x + 3 = x² – x – x² + 9; x² + 4x + 3 + x – 9 = 0; x² + 5x – 6 = 0; D = 5² – 4 • 1 • (–6) = 25 + 24; √D = 7; х1 = (-5+7)/2 = 1; х2 = (-5+7)/2 = –6.