What are the solutions to the equation roots x^6-x^3-2 ?

The solutions to the equation roots x^6-x^3-2 are

Find the zeros of roots x^6-x^3-2

The zeros of roots x^6-x^3-2 are

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roots

x^{6} - x^{3} - 2

Solution steps

x^{6} - x^{3} - 2

The roots are the intercepts with the x-axis

(y = 0)

x^{6} - x^{3} - 2 = 0

Rewrite the equation with

u = x^{3}

and

u^{2} = x^{6}

u^{2} - u - 2 = 0

Solve

u^{2} - u - 2 = 0 : u = 2, u = - 1

u = 2, u = - 1

Substitute back

u = x^{3},

solve for

x

Solve

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

The solutions are

z^{3} = (- 1 - 3 i)

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

x^{4} + 6 x^{3} - 3 x^{2} - 24 x - 4 = 0

x^{4} - 6 x^{3} + 2 x^{2} + 26 x + 17

9 x^{3} + 9 x^{2} - x - 1 = 0

What are the solutions to the equation roots x^6-x^3-2 ?
The solutions to the equation roots x^6-x^3-2 are
Find the zeros of roots x^6-x^3-2
The zeros of roots x^6-x^3-2 are