Question

{X^2+y^2=10, {xy=3 Помогите решить Посмотреть ответы oganesbagoyan oganesbagoyan {x²+y²=10, {xy= 3.               Ответ:  (-3 , -1) ;  (-1 , -3) , (1 , 3) , (3, 1) . Объяснение:   xy = 3 > 0  ⇒ переменные  x,y одного знака ;                                          уравнения системы симметричны относительно переменных  ⇒ если  (a;b) решение системы  , то  пара  (b; a) тоже решение --------------- {x²+y²= 10, {x²y² = 9 . x² и  y²  корни уравнения t² - 10t +9 =0 ⇒ t₁ =9 ; t₂= 1. { x²=9;       {x=±3 ;               {y² =1 .       {y =±1 . ответ:  (-3 , -1) ;  (-1 , -3) , (1 , 3) , (3, 1) . mathgenius mathgenius Ответ: (3;1) ; (1;3) ; (-1;-3) ; (-3;-1). Объяснение: Умножаем второе уравнение на 2 . 2xy=6  (y = 3/x) Прибавим второе уравнение к первому и вычтем из первого второе : x^2+2xy+y^2=16 x^2-2xy+y^2=4 (x+y)^2=16 (x-y)^2=4 x+y=+-4 x-y=+-2 Cкладываем: 2x= (+-4 +(+-2)) x= +-2+ (+-1) x1=3 ; y1=3/3=1 x2=1; y2=3/1=3 x3=-1 ; y3=3/-1=-3 x4=-3 ;  y4=3/-3=-1 Новые вопросы в Алгебра 5-2(х-1)=4-х Помогите решыть ! 3(x-2)=x+2 помогите решыть розвʼяжіть систему рівнянь х-у=5 х+у=1 А.(-2;3) Б.(6;1) В.(-2;3) Г.(3;-2) Басейн наповнюється двома трубами за 4 години. За скільки годин наповнить цей басейн кожна труба окремо, коли відомо, що продуктивність однієї з них у … 2,5 рази вища від продуктивності другої? Допоможіть будь ласка y = x ^ 2 - 8|x| + 7 зробіть графік​ 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 решения системы уравнений, выше представленного два разных ответа. Давайте разберем оба решения:

1. Первый ответ: Уравнения системы:

1. x² + y² = 10
2. xy = 3

Из уравнения 2 получаем, что xy > 0, что означает, что переменные x и y имеют одинаковые знаки. Таким образом, уравнения симметричны относительно переменных. Если (a, b) является решением системы, то пара (b, a) также является решением.

Теперь найдем значения x и y, подставив xy = 3 в первое уравнение: x² + y² = 10 (x^2)(y^2) = 10(xy) - 3² x^2y^2 = 10(3) - 9 x^2y^2 = 30 - 9 x^2y^2 = 21

Теперь у нас есть два уравнения:

1. xy = 3
2. x^2y^2 = 21

Мы знаем, что xy = 3 > 0, значит, x и y оба положительные или оба отрицательные. Решая эти уравнения, мы получим четыре возможных решения: (-3, -1), (-1, -3), (1, 3), (3, 1).

2. Второй ответ: Уравнения системы:

1. x² + y² = 10
2. x²y² = 9

Мы умножаем второе уравнение на 2: 2x²y² = 18

Теперь у нас есть два уравнения:

1. x² + y² = 10
2. 2x²y² = 18

Мы знаем, что x²y² = 9, поэтому подставим это значение во второе уравнение: 2(9) = 18

Условие выполнено, значит, у нас есть еще два возможных решения: (3, 1), (1, 3).

В итоге, оба решения действительны, и ответ на систему уравнений состоит из четырех точек: (-3, -1), (-1, -3), (1, 3), (3, 1).