Question

{x² + y ² = 50{ x y = 7​ Смотреть ответ avilov41 avilov41 Ответ: (1;7) ,(7;1) ,(-1;-7) ,(-7;-1) Пошаговое объяснение: Умножим второе уравнение на два и сложим с первым, получим полный квадрат: {x^2+y^2=50 {2xy  =14 x^2+2xy+y^2=64 (x+y)^2+64 Отсюда   { x+y=8            { x+y=-8                                   { xy=7                {xy= 7 Составляем квадратное уравнение используя формулы Виета: t^2-8t+7=0           z^2+8z+7=0  Решаем квадратные уравнения по  обратной теореме Виета ( подбором) t1=7; t2=1             z1=-1; z2=-7 Отсюда получаем  четыре пары  решений системы: (1;7) ,(7;1) ,(-1;-7), (-7:-1) Новые вопросы в Математика 8848-(a*2):5=5698-54 Помогите Найти интегралы пожалуйста Найти интегралы пожалуйста...) 5. Задача по теории вероятностей В лотерее 2000 билетов. На один билет падает выигрыш 100 руб., на четыре билета - выигрыш по 50 руб., на 10 билетов в … ыигрыш по 20,на 20 билетов выигрыш по 10 руб., на 165 - по 5 руб.,на 400 билетов - по 1 руб. Остальные билеты невыигрышные. Какова вероятность выиграть по билету не менее 10 руб? 4. Задача по комбинаторике На турнир по волейболу приехало 32 команды. Их необходимо разделить на 4 подгруппы. Сколькими способами можно это сделать? 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

Конечно, я могу помочь вам с математическими вопросами. Давайте начнем с вашего первого вопроса:

У вас есть система уравнений:

1. $x^2 + y^2 = 50$
2. $xy = 7$

Вы хотите найти решения этой системы. Вы уже правильно начали, умножив второе уравнение на 2 и сложив его с первым:

$x^2 + 2xy + y^2 = 64$

Вы заметили, что это является полным квадратом и может быть записано как $(x + y)^2$:

$(x + y)^2 = 64$

Теперь вы можете найти два возможных значения для $x + y$:

1. $x + y = 8$
2. $x + y = -8$

Из второго уравнения в системе вы знаете, что $xy = 7$. Теперь вы можете использовать эти два уравнения для нахождения значений $x$ и $y$. Подставив значения $x + y$, вы можете найти $x$ и $y$ для каждой из этих двух случаев.

1. $x + y = 8$: Выразите, например, $y = 8 - x$, и подставьте в уравнение $xy = 7$: $x(8 - x) = 7$ Решите это квадратное уравнение и найдите два корня для $x$, а затем соответствующие значения $y$.

2. $x + y = -8$: Подход аналогичен, но у вас будет $y = -8 - x$, и опять подставьте в уравнение $xy = 7$.

После решения обоих случаев вы получите все четыре пары решений для данной системы уравнений: $(1, 7)$, $(7, 1)$, $(-1, -7)$, $(-7, -1)$.

Если у вас есть другие вопросы или вы хотите обсудить что-то еще, пожалуйста, дайте мне знать!