7. Найдите корни уравнения: a) 10x²+5x-0,6=0; б) 7x²+8x+1=0; в) 2x²-3x+2=0; г) x²+6=5x; д) 5y²-4y=1; е) 2-3x=5x².

a) 10x² + 5x - 0.6 = 0 D = 5² - 4 * 10 * (-0.6) = 25 + 24 = 49 x₁ = (-5 + √49) / (2 * 10) = (-5 + 7) / 20 = 2/20 = 0.1 x₂ = (-5 - √49) / (2 * 10) = (-5 - 7) / 20 = -12/20 = -0.6 Ответ: x = 0.1, x = -0.6 б) 7x² + 8x + 1 = 0 D = 8² - 4 * 7 * 1 = 64 - 28 = 36 x₁ = (-8 + √36) / (2 * 7) = (-8 + 6) / 14 = -2/14 = -1/7 x₂ = (-8 - √36) / (2 * 7) = (-8 - 6) / 14 = -14/14 = -1 Ответ: x = -1/7, x = -1 в) 2x² - 3x + 2 = 0 D = (-3)² - 4 * 2 * 2 = 9 - 16 = -7 D < 0, поэтому корней нет. г) x² + 6 = 5x => x² - 5x + 6 = 0 D = (-5)² - 4 * 1 * 6 = 25 - 24 = 1 x₁ = (5 + √1) / 2 = (5 + 1) / 2 = 3 x₂ = (5 - √1) / 2 = (5 - 1) / 2 = 2 Ответ: x = 3, x = 2 д) 5y² - 4y = 1 => 5y² - 4y - 1 = 0 D = (-4)² - 4 * 5 * (-1) = 16 + 20 = 36 y₁ = (4 + √36) / (2 * 5) = (4 + 6) / 10 = 10/10 = 1 y₂ = (4 - √36) / (2 * 5) = (4 - 6) / 10 = -2/10 = -0.2 Ответ: y = 1, y = -0.2 е) 2 - 3x = 5x² => 5x² + 3x - 2 = 0 D = 3² - 4 * 5 * (-2) = 9 + 40 = 49 x₁ = (-3 + √49) / (2 * 5) = (-3 + 7) / 10 = 4/10 = 0.4 x₂ = (-3 - √49) / (2 * 5) = (-3 - 7) / 10 = -10/10 = -1 Ответ: x = 0.4, x = -1