Решите уравнение x|x| − 9x − 10 = 0.
А) $-1; 10; \frac{-9 - \sqrt{41}}{2}; \frac{-9 + \sqrt{41}}{2}$
Б) $10; \frac{-9 - \sqrt{41}}{2}; \frac{-9 + \sqrt{41}}{2}$
В) $-1; \frac{-9 - \sqrt{41}}{2}$
Г) −1; 10
x|x| − 9x − 10 = 0
1) x ≥ 0
x * x − 9x − 10 = 0
$x^2 - 9x - 10 = 0$
$D = b^2 - 4ac = (-9)^2 - 4 * 1 * (-10) = 81 + 40 = 121 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{9 + \sqrt{121}}{2 * 1} = \frac{9 + 11}{2} = \frac{20}{2} = 10$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{9 - \sqrt{121}}{2 * 1} = \frac{9 - 11}{2} = \frac{-2}{2} = -1 < 0$ − не удовлетвояет условию, так как x ≥ 0
2) x < 0
x * (−x) − 9x − 10 = 0
$-x^2 - 9x - 10 = 0$
$D = b^2 - 4ac = (-9)^2 - 4 * (-1) * (-10) = 81 - 40 = 41 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{9 + \sqrt{41}}{2 * (-1)} = \frac{9 + \sqrt{41}}{-2} = -\frac{9 + \sqrt{41}}{2} = \frac{-9 - \sqrt{41}}{2}$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{9 - \sqrt{41}}{2 * (-1)} = \frac{9 - \sqrt{41}}{-2} = -\frac{9 - \sqrt{41}}{2} = \frac{-9 + \sqrt{41}}{2}$
Ответ: Б) $10; \frac{-9 - \sqrt{41}}{2}; \frac{-9 + \sqrt{41}}{2}$.
Пожауйста, оцените решение
