Question

Решите систему неравенств: {x^2+4x-5>0 { 5-3(x+1)>x Смотреть ответ orudzovasabrina orudzovasabrina Ответ: (1;4) Объяснение: {x^2+4 x-5>0 {x^2-2x-8<0 Новые вопросы в Алгебра два муравья без остановочно ползают туда-сюда по линейке длиной 15 см скорость первого муравья 3 см в минуту А второго 5 см в минуту стартуют они с с … противоположных концов линейки Сколько раз встретятся муравьи за один час? Составьте числовое выражение и найдите его назначение №1. Для школи придбали 15 хокейних клю­чок і 5 м'ячів, заплативши за всю покупку 64 грн. Скільки коштує ключка і скільки коштує м'яч. коли відомо, що … 5 ключок дорожчі за 2 м'ячі на 3 грн? №2. За 4 години їзди автомобілем і 7 годин їзди поїздом туристи проїхали 640 км. Яка швидкість поїзда, якщо вона на 5 км/год більша від швидкості автомобіля? Помогите пожалуйста очень срочно Сделайте пожалуйста чтобы было понятно Я сделаю как лучший ответ 10. Задайте формулою функцію, графік якої зображено на рисунку. А)x=3 Б)y=-3 В)y=-3+x Г)y=3-x спростіть вираз (с-4)²-(3-с)²​ Предыдущий Следующий Вместе мы знаем больше Этот сайт использует cookies Политика Cookies . Вы можете указать условия хранения и доступ к cookies в своем браузере. 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Answer 1

Давайте начнем с решения системы неравенств:

1. x^2 + 4x - 5 > 0

Сначала найдем корни квадратного уравнения x^2 + 4x - 5 = 0. Мы можем использовать квадратное уравнение, чтобы найти эти корни:

x^2 + 4x - 5 = 0

Для нахождения корней, мы можем использовать квадратное уравнение:

(x - 1)(x + 5) = 0

Отсюда получаем два корня:

x1 = 1 x2 = -5

Тепер мы можем использовать эти корни, чтобы разбить числовую прямую на интервалы и определить знак выражения x^2 + 4x - 5 в каждом из них.

Интервал 1: (-бесконечность, -5) Выберем точку в этом интервале, например, x = -6: x^2 + 4x - 5 = (-6)^2 + 4(-6) - 5 = 36 - 24 - 5 = 7

Так как 7 > 0, то на этом интервале выражение x^2 + 4x - 5 > 0.

Интервал 2: (-5, 1) Выберем точку в этом интервале, например, x = 0: x^2 + 4x - 5 = (0)^2 + 4(0) - 5 = -5

Так как -5 < 0, то на этом интервале выражение x^2 + 4x - 5 < 0.

Интервал 3: (1, +бесконечность) Выберем точку в этом интервале, например, x = 2: x^2 + 4x - 5 = (2)^2 + 4(2) - 5 = 4 + 8 - 5 = 7

Так как 7 > 0, то на этом интервале выражение x^2 + 4x - 5 > 0.

Теперь перейдем ко второму неравенству:

2. 5 - 3(x + 1) > x

Раскроем скобки и упростим:

5 - 3x - 3 > x

Переносим все члены на одну сторону неравенства:

5 - 3 - 3x - x > 0

2 - 4x > 0

-4x > -2

Теперь разделим обе стороны на -4, при этом помня, что при делении на отрицательное число неравенство меняет направление:

x < 1/2

Итак, мы получили решение второго неравенства.

Теперь объединим решения обоих неравенств. Поскольку первое неравенство выполняется на интервалах (-бесконечность, -5) и (1, +бесконечность), а второе неравенство на интервале (-бесконечность, 1/2), то общее решение будет пересечением этих интервалов, то есть интервалом (1/2, +бесконечность).

Итак, решение системы неравенств:

{x^2 + 4x - 5 > 0 {5 - 3(x + 1) > x

это интервал (1/2, +бесконечность).