What are the solutions to the equation x^6-2x^3+1=0 ?

The solutions to the equation x^6-2x^3+1=0 are x=1,x=-1/2+(sqrt(3))/2 i,x=-1/2-(sqrt(3))/2 i

Find the zeros of x^6-2x^3+1=0

The zeros of x^6-2x^3+1=0 are x=1,x=-1/2+(sqrt(3))/2 i,x=-1/2-(sqrt(3))/2 i

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x^{6} - 2 x^{3} + 1 = 0

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

Solution steps

x^{6} - 2 x^{3} + 1 = 0

Rewrite the equation with

u = x^{3}

and

u^{2} = x^{6}

u^{2} - 2 u + 1 = 0

Solve

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

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

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

(x^{2} - 4) (x^{2} + 1) (x - 3) = 0

3 x^{3} + 5 x^{2} - 4 x - 4 = 0

x, x^{3} y - y^{2} = 3

x^{2} (x^{2} + 4) (x^{2} + 16) - 100 = 0

x^{4} - 2 x + 1 = 0

What are the solutions to the equation x^6-2x^3+1=0 ?
The solutions to the equation x^6-2x^3+1=0 are x=1,x=-1/2+(sqrt(3))/2 i,x=-1/2-(sqrt(3))/2 i
Find the zeros of x^6-2x^3+1=0
The zeros of x^6-2x^3+1=0 are x=1,x=-1/2+(sqrt(3))/2 i,x=-1/2-(sqrt(3))/2 i