What are the solutions to the equation 27x^3-1=0 ?

The solutions to the equation 27x^3-1=0 are x= 1/3 ,x=-1/6+1/(2sqrt(3))i,x=-1/6-1/(2sqrt(3))i

Find the zeros of 27x^3-1=0

The zeros of 27x^3-1=0 are x= 1/3 ,x=-1/6+1/(2sqrt(3))i,x=-1/6-1/(2sqrt(3))i

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27 x^{3} - 1 = 0

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

Solution steps

27 x^{3} - 1 = 0

Move

1

to the right side

27 x^{3} = 1

Divide both sides by

27

x^{3} = \frac{1}{27}

For

x^{3} = f (a)

the solutions are

Simplify

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

4 x^{2} - 9 = (2 x^{3}) (2 x - 3)

4 x^{4} - 64 x^{2} = 0

8 x^{3} = (- 2 x) (A)

9 x^{3} - 18 x^{2} - 4 x + 8 = 0

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

What are the solutions to the equation 27x^3-1=0 ?
The solutions to the equation 27x^3-1=0 are x= 1/3 ,x=-1/6+1/(2sqrt(3))i,x=-1/6-1/(2sqrt(3))i
Find the zeros of 27x^3-1=0
The zeros of 27x^3-1=0 are x= 1/3 ,x=-1/6+1/(2sqrt(3))i,x=-1/6-1/(2sqrt(3))i