6. Решите уравнение: a) x²+x=0; б) x²-4x+3=0; в) 5x²+14x-3=0; г) x²-2x-2=0; д) 6x=3x²; е) x²-5x+4=0; ж) 7x²-4=0; з) 3x²-x+2=0.

a) x² + x = 0 x(x + 1) = 0 x = 0 или x + 1 = 0 => x = -1 Ответ: x = 0, x = -1 б) x² - 4x + 3 = 0 D = (-4)² - 4 * 1 * 3 = 16 - 12 = 4 x₁ = (4 + √4) / 2 = (4 + 2) / 2 = 3 x₂ = (4 - √4) / 2 = (4 - 2) / 2 = 1 Ответ: x = 3, x = 1 в) 5x² + 14x - 3 = 0 D = 14² - 4 * 5 * (-3) = 196 + 60 = 256 x₁ = (-14 + √256) / (2 * 5) = (-14 + 16) / 10 = 2/10 = 1/5 = 0.2 x₂ = (-14 - √256) / (2 * 5) = (-14 - 16) / 10 = -30/10 = -3 Ответ: x = 0.2, x = -3 г) x² - 2x - 2 = 0 D = (-2)² - 4 * 1 * (-2) = 4 + 8 = 12 x₁ = (2 + √12) / 2 = (2 + 2√3) / 2 = 1 + √3 x₂ = (2 - √12) / 2 = (2 - 2√3) / 2 = 1 - √3 Ответ: x = 1 + √3, x = 1 - √3 д) 6x = 3x² 3x² - 6x = 0 3x(x - 2) = 0 x = 0 или x - 2 = 0 => x = 2 Ответ: x = 0, x = 2 е) x² - 5x + 4 = 0 D = (-5)² - 4 * 1 * 4 = 25 - 16 = 9 x₁ = (5 + √9) / 2 = (5 + 3) / 2 = 4 x₂ = (5 - √9) / 2 = (5 - 3) / 2 = 1 Ответ: x = 4, x = 1 ж) 7x² - 4 = 0 7x² = 4 x² = 4/7 x = ±√(4/7) = ±2/√7 = ±2√7 / 7 Ответ: x = 2√7 / 7, x = -2√7 / 7 з) 3x² - x + 2 = 0 D = (-1)² - 4 * 3 * 2 = 1 - 24 = -23 D < 0, поэтому корней нет.