4. Решите уравнение: 1) 4(3y + 1)² - 27 = (4y + 9)(4y - 9) + 2(5y + 2)(2y - 7); 2) (4x-3)² - 25x² = 0; 3) (x - 2)² + (x + 7)² = 2(2-x)(x + 7).

1) 4(3y + 1)² - 27 = (4y + 9)(4y - 9) + 2(5y + 2)(2y - 7); 4(9y² + 6y + 1) - 27 = 16y² - 81 + 2(10y² - 31y - 14) 36y² + 24y + 4 - 27 = 16y² - 81 + 20y² - 62y - 28 36y² + 24y - 23 = 36y² - 62y - 109 24y + 62y = -109 + 23 86y = -86 y = -1 2) (4x - 3)² - 25x² = 0; 16x² - 24x + 9 - 25x² = 0 -9x² - 24x + 9 = 0 9x² + 24x - 9 = 0 3x² + 8x - 3 = 0 D = 8² - 4 * 3 * (-3) = 64 + 36 = 100 x1 = (-8 + 10) / (2 * 3) = 2 / 6 = 1/3 x2 = (-8 - 10) / (2 * 3) = -18 / 6 = -3 3) (x - 2)² + (x + 7)² = 2(2 - x)(x + 7); x² - 4x + 4 + x² + 14x + 49 = 2(4 + 14 - 2x - x²) 2x² + 10x + 53 = 8 + 28 - 4x - 2x² 4x² + 14x + 17 = 0 D = 14² - 4 * 4 * 17 = 196 - 272 = -76 < 0 Нет корней