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Консультация № 199305
12.10.2020, 20:12
0.00 руб.
0
2
1
Уважаемые эксперты! Здравствуйте. Пожалуйста, помогите ответить на вопрос:
Найдите все значения параметра a, при каждом из которых система неравенств имеет единственное решение на отрезке [3;4].
[formula]\left\{\begin{matrix}
ax\geq 2,\\
\sqrt{x-1}>a,\\
3x\leq 2a+11
\end{matrix}\right.[/formula]
Найдите все значения параметра a, при каждом из которых система неравенств имеет единственное решение на отрезке [3;4].
[formula]\left\{\begin{matrix}
ax\geq 2,\\
\sqrt{x-1}>a,\\
3x\leq 2a+11
\end{matrix}\right.[/formula]
Обсуждение
12.10.2020, 20:14
общий
Извините, формула не сработала почему-то. Прикрепляю фотографией систему неравенств.
14.10.2020, 17:20
общий
это ответ
Здравствуйте, Dan2206!
Дана система из 3х неравенств : a·x >= 2 ; [$8730$](x - 1) > a ; 3·x <= 2·a + 11
Требуется найти все значения параметра a, при каждом из которых система неравенств имеет единственное решение на отрезке [3;4].
Решение : Можно использовать вычислительное приложение Маткад (ссылка) либо Онлайн-решатель, чтобы "методом тыка" найти искомый параметр. Но это будет не совсем математическое решение.
Воспользуемся узостью диапазона x-значений и решим неравенства, чтоб получить диапазон значений a-параметра, при котором
3 <= x <= 4 . Это проще делать графически. На рисунке ниже я показал, что параметр "a" изменяется в диапазоне
0,5 <= x <= 1,73
Теперь строим графики x(a) с пределами 0,4 <= a <= 1,8 (чуть шире минимально-необходимого для наглядности и надёжности).
На графике видно, что только при a = 0,5 система имеет единственное решение x = 4 .
При a > 0,5 система имеет уже множество решений.
При a < 0,5 система не имеет решений.
Ответ : a = 0,5
Дана система из 3х неравенств : a·x >= 2 ; [$8730$](x - 1) > a ; 3·x <= 2·a + 11
Требуется найти все значения параметра a, при каждом из которых система неравенств имеет единственное решение на отрезке [3;4].
Решение : Можно использовать вычислительное приложение Маткад (ссылка) либо Онлайн-решатель, чтобы "методом тыка" найти искомый параметр. Но это будет не совсем математическое решение.
Воспользуемся узостью диапазона x-значений и решим неравенства, чтоб получить диапазон значений a-параметра, при котором
3 <= x <= 4 . Это проще делать графически. На рисунке ниже я показал, что параметр "a" изменяется в диапазоне
0,5 <= x <= 1,73
Теперь строим графики x(a) с пределами 0,4 <= a <= 1,8 (чуть шире минимально-необходимого для наглядности и надёжности).
На графике видно, что только при a = 0,5 система имеет единственное решение x = 4 .
При a > 0,5 система имеет уже множество решений.
При a < 0,5 система не имеет решений.
Ответ : a = 0,5
5
Огромное спасибо!
Форма ответа
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