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{3х-5y=14{2x-7y=2Способом сложения Смотреть ответ Pororo923 Pororo923 Способ сложения 5x-12y=16 5x-12y-16=0 Другой способ {3x-5y=14 {2x-7y=2 {x=14/3 + 5/3 y {2x-7y=2 2(14/3 +5/3 y)-7y=2 y=2 x=14/3 + 5/3 *2 x=8 (x,y)=(8,2) Новые вопросы в Алгебра как найти наибольшее или наименьшее значение многочлена или выражения? у класс! сроооооооооооооооооооооооооооооооооооооооочноооооооооооо! помогите срочно пожалуйста ​ СРОЧНО!!! Приведите выражение к многочлену стандартного вида, используя формулы сокращённого умножения:(1/2m+4n)^2 5. Подайте тричлен у чигляді У зигляді квадрата двочлена: квадрата двочлена: а² + 8 +16.​ ДУЖЕ ТЕРМІНОВО! Розв'язати систему рiвнянь ​ 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

Для того чтобы найти наибольшее или наименьшее значение многочлена или выражения, следует выполнить следующие шаги:

1. Представьте многочлен или выражение в стандартной форме. Это означает упорядочить слагаемые по убыванию степеней переменных.

2. Для многочленов с одной переменной, наибольшее или наименьшее значение достигается на экстремальных точках или на концах интервала, на котором ищется значение. Вы можете найти эти точки, приравняв производную многочлена к нулю и решив полученное уравнение.

3. Для многочленов с несколькими переменными, может понадобиться использовать методы оптимизации, такие как метод Лагранжа или метод множителей Лагранжа, чтобы найти экстремумы.

4. Если многочлен или выражение задано в числовом виде (все переменные заменены на конкретные значения), вы можете просто вычислить значение выражения.

Теперь рассмотрим примеры:

1. Найти наибольшее и наименьшее значение многочлена P(x) = 3x^2 - 12x + 8 на интервале [0, 4]:

   a) Найдем экстремальные точки, приравнивая производную многочлена к нулю: P'(x) = 6x - 12 6x - 12 = 0 6x = 12 x = 2

   б) Проверим значения многочлена на концах интервала: При x = 0: P(0) = 3(0)^2 - 12(0) + 8 = 8 При x = 4: P(4) = 3(4)^2 - 12(4) + 8 = 8

   в) Таким образом, наименьшее значение равно 8 (достигается при x = 0), а наибольшее значение также равно 8 (достигается при x = 2 и x = 4).

2. Приведем выражение (1/2m + 4n)^2 к многочлену стандартного вида:

   (1/2m + 4n)^2 = (1/2m + 4n) * (1/2m + 4n) Используем формулу сокращенного умножения для двух биномов: (a + b)^2 = a^2 + 2ab + b^2.

   (1/2m + 4n)^2 = (1/2m)^2 + 2 * (1/2m) * 4n + (4n)^2 = 1/4m^2 + 4n/m + 16n^2

3. Найдем наибольшее и наименьшее значение многочлена Q(x, y) = 3x + 2y в области ограниченной системой уравнений:

   { x + y = 5 { x - y = 3

   a) Решим систему уравнений: Добавим оба уравнения, чтобы устранить y: (x + y) + (x - y) = 5 + 3 2x = 8 x = 4 Подставим значение x в любое из уравнений для нахождения y: x + y = 5 4 + y = 5 y = 5 - 4 y = 1

   б) Теперь найдем значения многочлена Q(x, y) при (x, y) = (4, 1): Q(4, 1) = 3(4) + 2(1) = 12 + 2 = 14

   в) Таким образом, наибольшее значение многочлена равно 14, а наименьшее значение тоже равно 14.

Обратите внимание, что второй и третий примеры были приведены для демонстрации общего подхода к нахождению наибольшего и наименьшего значения многочлена или выражения в определенной области. В реальных задачах значения могут различаться в зависимости от конкретных условий и выражений.