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Задать вопрос экспертам

Консультация № 176880

24.02.2010, 01:01

0.00 руб.

26.02.2010, 11:52

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Образование

доброго времени суток!помогите пожалуйста с заданием:

Обсуждение

давно

Орловский Дмитрий

Мастер-Эксперт
319965
1463

24.02.2010, 13:48

общий

это ответ

Здравствуйте, cookie1992.

Данная система относится к классу симметричных. Такие системы обычно упрощаются после замены
u=x+y, v=xy
Отсюда находим x²+y²=(x+y)²-2xy=u²-2v
и в новых переменных система принимает вид
u²-2v+u=32
12u=7v

Из второго уравнения находим v=12u/7 и подставляем в первое. Получаем квадратное уравнение
7u²-17u-224=0
с корнями u=7 и u=-32/7

1) u=7, v=12u/7=12
Далее решаем систему типа Виета
x+y=7
xy=12
Она сводится к квадратному уравнению x²-7x+12=0, которое дает два решения
x=3 (y=4) и x=4 (y=3

2) u=-32/7, v=12u/7=-384/49
Далее решаем систему типа Виета
x+y=-32/7
xy=-384/49
Она сводится к квадратному уравнению 49x²+224x-384=0, которое дает два решения
x=(-16+8[$8730$]10)/7 (y=(-16-8[$8730$]10)/7) и
x=(-16-8[$8730$]10)/7 (y=(-16=8[$8730$]10)/7)

Ответ:
(3;4), (4;3), ((-16+8[$8730$]10)/7;(-16-8[$8730$]10)/7), ((-16-8[$8730$]10)/7;(-16+8[$8730$]10)/7)

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