Step-by-step explanation:
x^3 is a perfect cube, 8 is a perfect cube, so we use difference of cubes.
[tex] {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]
Cube root of x^3 is x.
Cube root of 8 is 2
So
a=x
b= 2.
[tex](x - 2)( {x}^{2} - 2x + 4)[/tex]
Set these equations equal to zero
[tex]x - 2 = 0[/tex]
[tex]x = 2[/tex]
[tex] {x}^{2} - 2x + 4 = 0[/tex]
If we do the discriminant, we get a negative answer so we would have two imaginary solutions,
Thus the only real root is 2.
If you want imaginary solutions, apply the quadratic formula.
[tex]1 + i \sqrt{ 3 } [/tex]
and
[tex]1 - i \sqrt{3} [/tex]
