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Консультация № 190562
14.02.2017, 04:39
0.00 руб.
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3
1
Здравствуйте, уважаемые эксперты!
Объясните, пожалуйста, как самым простым способом решить неравенство
(x-4)(x-3)>=0 ?
Объясните, пожалуйста, как самым простым способом решить неравенство
(x-4)(x-3)>=0 ?
Обсуждение
14.02.2017, 06:28
общий
Адресаты:
Используйте метод интервалов. Он известен Вам?
Об авторе:
Facta loquuntur.
Facta loquuntur.
14.02.2017, 11:36
общий
Адресаты:
Или графически.
Что представляет собой функция (x-4)(x-3)=0 ?
Что представляет собой функция (x-4)(x-3)=0 ?
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
14.02.2017, 11:41
общий
это ответ
Здравствуйте, svrvsvrv!
Пусть дано неравенство
Решить его можно по-разному.
В левой части неравенства записаны два линейных относительно переменной
сомножителя. Их произведение будет неотрицательным, если оба множителя неотрицательны или оба множителя неположительны. В первом случае получим систему двух линейных неравенств
решением которой является промежуток
Во втором случае получим систему двух линейных неравенств
решением которой является промежуток
Решением заданного неравенства будет объединение указанных промежутков.
Можно использовать метод интервалов. Решим сначала уравнение
Корнями этого уравнения являются числа
Отметим эти числа на числовой прямой. Если 
то оба сомножителя в левой части заданного неравенства положительны и их произведение тоже положительно. Если 
то 
и произведение отрицательно. Если 
то оба сомножителя отрицательны и произведение положительно. Поскольку заданное неравенство - нестрогое, то ему удовлетворяют и корни уравнения. Значит, решением заданного неравенства будет объединение промежутков 
и
Пусть дано неравенство
Решить его можно по-разному.
В левой части неравенства записаны два линейных относительно переменной
сомножителя. Их произведение будет неотрицательным, если оба множителя неотрицательны или оба множителя неположительны. В первом случае получим систему двух линейных неравенстврешением которой является промежуток
Во втором случае получим систему двух линейных неравенств
решением которой является промежуток
Решением заданного неравенства будет объединение указанных промежутков.
Можно использовать метод интервалов. Решим сначала уравнение
Корнями этого уравнения являются числа
Отметим эти числа на числовой прямой. Если то оба сомножителя в левой части заданного неравенства положительны и их произведение тоже положительно. Если то и произведение отрицательно. Если то оба сомножителя отрицательны и произведение положительно. Поскольку заданное неравенство - нестрогое, то ему удовлетворяют и корни уравнения. Значит, решением заданного неравенства будет объединение промежутков и
5
Большое спасибо за консультацию. Очень подробно и доступно.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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