What are the solutions to the equation x^6+4x^3+8=0 ?

The solutions to the equation x^6+4x^3+8=0 are

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^6+4x^3+8=0

x^{6} + 4 x^{3} + 8 = 0

x = 1 + i, x = \frac{- 1 - 3}{2} + i \frac{- 1 + 3}{2}, x = \frac{- 1 + 3}{2} + i \frac{- 1 - 3}{2}, x = 1 - i, x = \frac{- 1 + 3}{2} + i \frac{1 + 3}{2}, x = \frac{- 1 - 3}{2} + i \frac{1 - 3}{2}

Solution steps

x^{6} + 4 x^{3} + 8 = 0

Rewrite the equation with

u = x^{3}

and

u^{2} = x^{6}

u^{2} + 4 u + 8 = 0

Solve

u^{2} + 4 u + 8 = 0 : u = - 2 + 2 i, u = - 2 - 2 i

u = - 2 + 2 i, u = - 2 - 2 i

Substitute back

u = x^{3},

solve for

x

Solve

x^{3} = - 2 + 2 i : x = 1 + i, x = \frac{- 1 - 3}{2} + i \frac{- 1 + 3}{2}, x = \frac{- 1 + 3}{2} + i \frac{- 1 - 3}{2}

Solve

x^{3} = - 2 - 2 i : x = 1 - i, x = \frac{- 1 + 3}{2} + i \frac{1 + 3}{2}, x = \frac{- 1 - 3}{2} + i \frac{1 - 3}{2}

The solutions are

x = 1 + i, x = \frac{- 1 - 3}{2} + i \frac{- 1 + 3}{2}, x = \frac{- 1 + 3}{2} + i \frac{- 1 - 3}{2}, x = 1 - i, x = \frac{- 1 + 3}{2} + i \frac{1 + 3}{2}, x = \frac{- 1 - 3}{2} + i \frac{1 - 3}{2}

x^{5} = x^{4}

x^{3} + 3 x^{2} - 4 x - 12 = 0

D, 2 b - hb = D^{3}

5 x^{4} - 9 x^{2} + 4

x^{3} - 5 x^{2} - 36 x = 0

What are the solutions to the equation x^6+4x^3+8=0 ?
The solutions to the equation x^6+4x^3+8=0 are
Find the zeros of x^6+4x^3+8=0
The zeros of x^6+4x^3+8=0 are