6. Решите уравнение.

а) x^2 + x = 0. Факторизуем: x(x + 1) = 0. Решения: x = 0, x = -1. б) x^2 - 4x + 3 = 0. D = (-4)^2 - 4*1*3 = 16 - 12 = 4. x1,2 = (4 ± √4) / 2 = (4 ± 2) / 2. x1 = 3, x2 = 1. в) x^2 + 5x + 4 = 0. D = 5^2 - 4*1*4 = 25 - 16 = 9. x1,2 = (-5 ± √9) / 2 = (-5 ± 3) / 2. x1 = -1, x2 = -4. г) 5x - 3x^2 = 0. Перепишем: x(5 - 3x) = 0. Решения: x = 0, x = 5/3. д) x^2 - 5x + 4 = 0. D = (-5)^2 - 4*1*4 = 25 - 16 = 9. x1,2 = (5 ± √9) / 2 = (5 ± 3) / 2. x1 = 4, x2 = 1.