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Задать вопрос экспертам

Консультация № 176318

26.01.2010, 16:24

42.39 руб.

0 1 1

Образование

Уважаемые эксперты, помогите пожалуйста решить уравнение:
|sin^3 x|+13(cos^3 x)-cos x = 0

Обсуждение

давно

Орловский Дмитрий

Мастер-Эксперт
319965
1463

26.01.2010, 21:38

общий

это ответ

Здравствуйте, STASSY.

1) sin x>=0
sin^3x+13cos^3x-cos x=0 (делим на cos^3x)
tg^3x+13-1/cos^2x=0
tg^3x+13-(1+tg^2x)=0
tg^3x-tg^2x+12=0
(tg x+2)(tg^2x-3tg x+6)=0
квадратное уравнение tg^2x-3tg x+6 имеет отрицательный дискриминант и решений не исмеет
отбираем корни уравнения tg x=-2 для которых sin x>=0:
x=-arctg2+pi+2 pi n (n - целое)
2) sin x<0
-sin^3x+13cos^3x-cos x=0 (делим на cos^3x)
-tg^3x+13-1/cos^2x=0
-tg^3x+13-(1+tg^2x)=0
tg^3x+tg^2x-12=0
(tg x-2)(tg^2x+3tg x+6)=0
квадратное уравнение tg^2x+3tg x+6 имеет отрицательный дискриминант и решений не исмеет
отбираем корни уравнения tg x=2 для которых sin x<0:
x=arctg2+pi+2 pi k (k - целое)
Ответ:
x=-arctg2+pi+2 pi n (n - целое)
x=arctg2+pi+2 pi k (k - целое)

5

Гениальное и простое решение, как я сама не догадалась))) Огромное пасиба

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