What are the solutions to the equation x^6-2=0 ?

The solutions to the equation x^6-2=0 are

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x^6-2=0

x^{6} - 2 = 0

x = 32, x = - 32, x = \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i

Solution steps

x^{6} - 2 = 0

Move

2

to the right side

x^{6} = 2

Rewrite the equation with

u = x^{2}

and

u^{3} = x^{6}

u^{3} = 2

Solve

u^{3} = 2 : u = 32, u = 32 \frac{- 1 + 3 i}{2}, u = 32 \frac{- 1 - 3 i}{2}

u = 32, u = 32 \frac{- 1 + 3 i}{2}, u = 32 \frac{- 1 - 3 i}{2}

Substitute back

u = x^{2},

solve for

x

Solve

x^{2} = 32 : x = 32, x = - 32

Solve

x^{2} = 32 \frac{- 1 + 3 i}{2} : x = \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i

Solve

x^{2} = 32 \frac{- 1 - 3 i}{2} : x = \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i

The solutions are

x = 32, x = - 32, x = \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = \frac{1}{2 ^{\frac{5}{6}}} - \frac{3}{2 ^{\frac{5}{6}}} i, x = - \frac{1}{2 ^{\frac{5}{6}}} + \frac{3}{2 ^{\frac{5}{6}}} i

x^{3} - 11 x^{2} + 43 x - 65

x^{4} + 9 x^{3} + 19 x^{2} - 18 x - 56 = 0

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

x^{3} - 9 x^{2} + 11 x + 21 = 0

- 1 x^{3} + 11 x^{2} - 32 x + 28 = 0

What are the solutions to the equation x^6-2=0 ?
The solutions to the equation x^6-2=0 are
Find the zeros of x^6-2=0
The zeros of x^6-2=0 are