Предмет: Алгебра, автор: ata221

Знатоки алгебры, срочно!
Найти корни уравнения
arctg(x {}^{3} - 27x - \sqrt{3} ) = - \frac{\pi}{3}
​

Приложения:
Simba2017: и то что я писала-подходит
Simba2017: скобку приравнивайте к -корню из 3 и решайте
shavrinatv: да
Simba2017: автор видно далек от темы, если поставил лишнюю "с"
ata221: невнимательность :)
ata221: давайте без оскорблений
ata221: я уже давно сам решил, буду благодарен, если скажете как можно удалить вопрос)
Simba2017: и сколько вышло?
ata221: 3 :)
Simba2017: дело ваше...

Ответы

Автор ответа: sharofat0
4

Ответ:

x_1=0

x_2=-27^1/2

x_3=27^1/2

Объяснение:

arctg( {x}^{3} - 27x - \sqrt{3 } ) = - \ \frac{\pi}{3}

- \frac{\pi}{2 } < - \frac{\pi}{3} < \frac{\pi}{2}

tg(arctga)=a

{x}^{3} - 27x - \sqrt{3 } = tg( - \frac{\pi}{3} )

{x}^{3} - 27x - \sqrt{3} = - \sqrt{3}

{x}^{3} - 27x = 0

x( {x}^{2} - 27) = 0

x_1=0

{x }^{2} - 27 = 0

{x}^{2} = 27

x = + - \sqrt{27}

x_2=-3×(3^1/2)

x_3=3×(3^1/2)

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