126. Решите уравнение: 1) (3x + 2)(x - 4) = 5; 2) (x + 1)(x – 2) - (4x - 3)(x + 5) = x(x – 9); 3) (3x – 5)² + (4x - 1)(4x + 1) = 29.

1) (3x + 2)(x - 4) = 5 3x² - 12x + 2x - 8 = 5 3x² - 10x - 13 = 0 D = (-10)² - 4 * 3 * (-13) = 100 + 156 = 256 x₁ = (10 + √256) / 6 = (10 + 16) / 6 = 26 / 6 = 13/3 x₂ = (10 - √256) / 6 = (10 - 16) / 6 = -6 / 6 = -1 Ответ: x = 13/3, x = -1 2) (x + 1)(x – 2) - (4x - 3)(x + 5) = x(x – 9) x² - 2x + x - 2 - (4x² + 20x - 3x - 15) = x² - 9x x² - x - 2 - 4x² - 17x + 15 = x² - 9x -3x² - 18x + 13 = x² - 9x -4x² - 9x + 13 = 0 4x² + 9x - 13 = 0 D = 9² - 4 * 4 * (-13) = 81 + 208 = 289 x₁ = (-9 + √289) / 8 = (-9 + 17) / 8 = 8 / 8 = 1 x₂ = (-9 - √289) / 8 = (-9 - 17) / 8 = -26 / 8 = -13/4 Ответ: x = 1, x = -13/4 3) (3x – 5)² + (4x - 1)(4x + 1) = 29 9x² - 30x + 25 + 16x² - 1 = 29 25x² - 30x + 24 = 29 25x² - 30x - 5 = 0 5x² - 6x - 1 = 0 D = (-6)² - 4 * 5 * (-1) = 36 + 20 = 56 x₁ = (6 + √56) / 10 = (6 + 2√14) / 10 = 3/5 + √14 / 5 x₂ = (6 - √56) / 10 = (6 - 2√14) / 10 = 3/5 - √14 / 5 Ответ: x = 3/5 + √14 / 5, x = 3/5 - √14 / 5