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Консультация № 200458
18.03.2021, 22:57
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Уважаемые эксперты! Пожалуйста, помогите:
сколько решений имеет |х+3|-а|х-1|=4
сколько решений имеет |х+3|-а|х-1|=4
Обсуждение
19.03.2021, 16:51
общий
это ответ
Здравствуйте, lana-gona!
Из заданного уравнения следует, что
Точки
и 
разбивают числовую прямую на три следующих промежутка:
1)
тогда уравнение имеет вид 
или 
при этом 
и 
2)
тогда уравнение имеет вид 
или 
при этом 
-- единственное значение параметра, при котором уравнение имеет решения на рассматриваемом промежутке;
3)
тогда уравнение имеет вид 
или 
при этом 
может быть любым.
График зависимости
показан в прикреплённом файле.
Если
то решениями уравнения являются значения 
Если
то решениями уравнения являются значения 
и 
Если
то решениями уравнения являются значения 
Если же
или 
то единственным решением уравнения является
Из заданного уравнения следует, что
Точки
и разбивают числовую прямую на три следующих промежутка:1)
тогда уравнение имеет вид или при этом и 2)
тогда уравнение имеет вид или при этом -- единственное значение параметра, при котором уравнение имеет решения на рассматриваемом промежутке;3)
тогда уравнение имеет вид или при этом может быть любым.График зависимости
показан в прикреплённом файле.Если
то решениями уравнения являются значения Если
то решениями уравнения являются значения и Если
то решениями уравнения являются значения Если же
или то единственным решением уравнения является
Прикрепленные файлы:
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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