Розділ 3. КВАДРАТНІ РІВНЯННЯ » 21.12

Розв’яжіть рівняння: 1) (x – 3)² = 2x – 3; x² – 6x + 9 – 2x + 3 = 0; x² – 8х + 12 = 0; D = (–8)² – 4 • 1 • 12 = 16; √D = 4; х1 = (8+4)/2 = 6; х2 = (8-4)/2 = 2. 2) 3(х + 1)² = 2x + 2; 3(x² + 2x + 1) – 2x – 2 = 0; 3x² + 6x + 3 – 2x – 2 = 0; 3x² + 4x + 1 = 0; D = 4² – 4 • 3 • 1 = 4; √D = 2; х1 = (-4+2)/(2•3) = (-2)/6 = –1/3; х2 = (-4-2)/6 = –1. 3) (x + 3)(х – 1) = 2x(x – 2) + 5; x² – x + 3х – 3 = 2x² – 4x + 5; x² + 2x – 3 – 2x2 + 4x – 5 = 0; –x² + 6x – 8 = 0; x² – 6x + 8 = 0; D = (–6)² – 4 • 1 • 8 = 4; √D = 2; х1 = (6+2)/2 = 4; х2 = (6-2)/2 = 2. 4) х(х – 3) – (x – 5)(x + 5) = (x + 1)²; x² – 3х – (x² – 25) = x² + 2x + 1; x² – 3х – x² + 25 = x² + 2x + 1; x² + 2x + 1 + 3х – 25 = 0; x² + 5x – 24 = 0; D = 5² – 4 • 1 • (–24) = 121; √D = 11; х1 = (-5+11)/2 = 6/2 = 3; х2 = (-5-11)/2 = –8.