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Консультация № 200488
25.03.2021, 14:55
0.00 руб.
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1
Здравствуйте, уважаемые эксперты! Прошу помочь:
решить abs(x-1)+abs(x+1)+abs(x-2)+ans(x+2)+...+abs(x-100)+abs(x+100)=200x
решить abs(x-1)+abs(x+1)+abs(x-2)+ans(x+2)+...+abs(x-100)+abs(x+100)=200x
Обсуждение
27.03.2021, 07:05
общий
это ответ
Здравствуйте, lana-gona!
Перепишем заданное уравнение так:
В левой части уравнения находится сумма двухсот неотрицательных слагаемых, из которых не больше одного может быть равно нулю. Поэтому правая часть уравнения должна быть положительной, то есть
Сразу заметим, что если
то заданное уравнение принимает вид
или
то есть обращается в тождество. Следовательно, заданное уравнение имеет решение 
Пусть, например,
Тогда заданное уравнение принимает вид
или
или 
откуда 
Но 
поэтому 
не является решением заданного уравнения. Вообще, такая ситуация возникает на любом из промежутков, где 
Поэтому решением уравнения является только
Перепишем заданное уравнение так:
В левой части уравнения находится сумма двухсот неотрицательных слагаемых, из которых не больше одного может быть равно нулю. Поэтому правая часть уравнения должна быть положительной, то есть
Сразу заметим, что если
то заданное уравнение принимает видили
то есть обращается в тождество. Следовательно, заданное уравнение имеет решение Пусть, например,
Тогда заданное уравнение принимает видили
или откуда Но поэтому не является решением заданного уравнения. Вообще, такая ситуация возникает на любом из промежутков, где Поэтому решением уравнения является только
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
27.03.2021, 11:14
общий
Адресаты:
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Об авторе:
Facta loquuntur.
Facta loquuntur.
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