Question

Неравенство (x−14)⋅(x+12)≤0 можно заменить системой неравенств. Выбери, какие системы годны для замены двойного неравенства: {x−14≥0 {x+12≤0 {x−14≤0 {x+12≤0 {x−14≤0 {x+12≥0 {x−14≥0 {x+12≥0 Смотреть ответ elena20092 elena20092 Ответ: 1) и 3) Объяснение: Для замены неравенства (x − 14) ⋅ (x + 12) ≤ 0 следует выбрать ту систему, которая обеспечивает отрицательный знак произведения, то есть 1) {x−14≥0    {x+12≤0 и 3) {x−14≤0    {x+12≥0 Дополнительно, решим неравенство Рассматривая систему неравенств 1), видим, что  она сводится к системе {х ≥ 14 {х ≤ -12 Очевидно, что данная система решений не имеет Рассматривая систему неравенств 3), видим, что  она сводится к системе {х ≤ 14 {х ≥ -12 Очевидно, что данная система имеет решение х ∈ [-12; 14] Новые вопросы в Алгебра Найти сумму, разность, произведение и частное двух комплексных чисел в алгебрической форме Вычислите интеграл. Тут по цифрам сверху 2 снизу -1, и потом куб Найдите производную функции просьба решить,заранее спасибо ​ Просьба решить,заранее спасибо ​ 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

Да, вы правильно поняли замену двойного неравенства (x−14)⋅(x+12)≤0 системой неравенств. Из данного неравенства следует, что произведение (x−14)⋅(x+12) должно быть меньше или равно нулю.

Произведение двух чисел будет меньше или равно нулю, если одно из чисел отрицательно, а другое неотрицательно, либо наоборот.

С учетом этого, правильные системы неравенств, которые могут заменить данное неравенство, это:

1. {x−14≥0, {x+12≤0 То есть, x ≥ 14 и x ≤ -12. Но эта система не имеет общих решений, так как нет числа, которое одновременно больше или равно 14 и меньше или равно -12.

2. {x−14≤0, {x+12≥0 То есть, x ≤ 14 и x ≥ -12. Эта система имеет решение x ∈ [-12, 14].

Оба случая соответствуют условию, что произведение (x−14)⋅(x+12) должно быть меньше или равно нулю.