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Консультация № 186852
22.11.2012, 12:24
79.10 руб.
0
1
1
Здравствуйте! Прошу помощи в следующем вопросе:Решить систему уравнений:(x^2)/y+(y^2)/x=12, 1/x+1/y=1/3. Заранее благодарен.
Обсуждение
22.11.2012, 13:11
общий
это ответ
Здравствуйте, Тимофеев Алексей Валентинович!
,
.
,
.
Подставим второе в первое:
,
,
,
.
Получилось квадратное уравнение относительно (x+y).
Его решения:
и
.
1. Соответственно, подставив первое выражение во второе уравнение(), получим
x + y = 12,
xy = 36.
Откуда
x = 6, y = 6.
2. x + y = -3,
xy = -9
,
,
,
откуда
.
Т.о. есть три решения:
,
.
,.,.Подставим второе в первое:
,,,.Получилось квадратное уравнение относительно (x+y).
Его решения:
и
.1. Соответственно, подставив первое выражение во второе уравнение(
), получимx + y = 12,
xy = 36.
Откуда
x = 6, y = 6.
2. x + y = -3,
xy = -9
,,,откуда
.Т.о. есть три решения:
,.
Форма ответа
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