Question

Решите системы уравнений,пожалуйста: 1. {(3 - 2x)^2 = 4y {(8 - 3x)^2 = 4y 2. {x^2 + y^2, {x*y = 1 Смотреть ответ Эндермен2007 Эндермен2007 {x^2+y^2=5,{xy=2; x^2+2xy+y^2-2xy=5,(x+y)^2-2xy=5;(x+y)^2-2*2=5;(x+y)^2=9; [x+y=-3,[x+y=3; [y=-3-x,[y=3-x; [-x(3+x)=2,[x(3-x)=2; [x^2+3x+2=0,[x^2-3x+2=0;x_1=-2, x_2=-1, x_3=1, x_4=2,y_1=-1, y_2=-2, y_3=2, y_4=1. {x^2-8xy+16y^2=25,{4y^2-xy=5; {(x-4y)^2=25,{y(4y-x)=5; [x-4y=-5,[x-4y=5; -y(x- 4y)=5,                                                           Вот так думаю[5y=5,[-5y=5;y_1=1, y_2=-1; [x-4=-5,[x-4*(-1)=5;x_1=-1, x_2=1. Новые вопросы в Алгебра Решите,то,что на фото пж За олівець і три зошити заплатили 8,8 грн, а за три олівці і зошит -7,2 грн. Скількі коштує один олівець і скільки один зошит Сколько корней имеет уравнение |x+1|=|2x-1| 0.6*75^0.5-0.6*27^0.5+1.5*12^0.5 спростіть вираз найдите координаты точки графика функции y=7x-5: 1)С одинаковыми ординатами 2) Сумма координат которой равна 19 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

Давайте по порядку решим каждую из систем уравнений:

1. {(3 - 2x)^2 = 4y {(8 - 3x)^2 = 4y

Для начала, заметим, что оба уравнения равны 4y, значит, они равны друг другу: (3 - 2x)^2 = (8 - 3x)^2

Раскроем квадраты: (9 - 12x + 4x^2) = (64 - 48x + 9x^2)

Теперь приведем уравнение к одному виду: 4x^2 - 12x + 9 = 64 - 48x + 9x^2

Перенесем все члены в одну часть уравнения: 4x^2 - 9x^2 - 12x + 48x - 9 - 64 = 0

Упростим: -5x^2 + 36x - 73 = 0

Теперь решим квадратное уравнение. Можно воспользоваться формулой дискриминанта, которая для уравнения вида ax^2 + bx + c = 0 имеет вид D = b^2 - 4ac.

D = 36^2 - 4*(-5)*(-73) D = 1296 - 1460 D = -164

Так как дискриминант отрицателен, у нас нет действительных корней.

2. {x^2 + y^2 = 5 {xy = 2

Теперь решим вторую систему уравнений методом подстановки. Подставим выражение для y из второго уравнения в первое: x^2 + (2/x)^2 = 5

Упростим уравнение: x^2 + 4/x^2 = 5

Теперь приведем уравнение к общему знаменателю: (x^4 + 4) / x^2 = 5

Перемножим обе части уравнения на x^2: x^4 + 4 = 5x^2

Теперь приведем уравнение в стандартную форму квадратного уравнения: x^4 - 5x^2 + 4 = 0

Решим полученное уравнение как квадратное относительно x^2: (x^2 - 1)(x^2 - 4) = 0

Теперь найдем значения x^2:

1. x^2 - 1 = 0 x^2 = 1 x = ±√1 x = ±1

2. x^2 - 4 = 0 x^2 = 4 x = ±√4 x = ±2

Теперь найдем значения y, используя второе уравнение:

1. Если x = 1: y = 2/x = 2/1 = 2 Таким образом, при x = 1, y = 2.

2. Если x = -1: y = 2/x = 2/(-1) = -2 Таким образом, при x = -1, y = -2.

3. Если x = 2: y = 2/x = 2/2 = 1 Таким образом, при x = 2, y = 1.

4. Если x = -2: y = 2/x = 2/(-2) = -1 Таким образом, при x = -2, y = -1.

Итак, решение системы уравнений: {x = 1, y = 2 {x = -1, y = -2 {x = 2, y = 1 {x = -2, y = -1

Теперь вернемся к остальным вопросам:

3. За олівець і три зошити заплатили 8,8 грн, а за три олівці і зошит -7,2 грн. Скільки коштує один олівець і скільки один зошит?

Пусть цена одного олівця равна x, а цена одного зошита равна y.

Из условия задачи у нас есть два уравнения: x + 3y = 8.8 3x + y = 7.2

Решим эту систему уравнений, например, методом сложения.

Первое уравнение умножим на 3, чтобы избавиться от коэффициента при y: 3(x + 3y) = 3 * 8.8 3x + 9y = 26.4

Теперь сложим это уравнение с вторым уравнением: (3x + 9y) + (3x + y) = 26.4 + 7.2 6x + 10y = 33.6

Теперь выразим x из последнего уравнения: 6x = 33.6 - 10y x = (33.6 - 10y) / 6 x = 5.6 - (5/3)y

Теперь подставим значение x в первое уравнение и решим его относительно y: (5.6 - (5/3)y) + 3y = 8.8 5.6 + (8/3)y = 8.8 (8/3)y = 3.2 y = (3.2 * 3) / 8 y = 1.2

Теперь найдем x, подставив значение y в любое из исходных уравнений, например, во второе: 3x + y = 7.2 3x + 1.2 = 7.2 3x = 7.2 - 1.2 3x = 6 x = 6 / 3 x =