what are the 3 solutions to (x^3-64=0)?

Question

i know one of them is x=4

Answer 1

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

x^3 - 64 = (x-4)(x^2 + 4x + 16)

the root of x - 4 .... is 4
the root of the other factor...
x^2 + 4x + 4 + 12
(x+2)^2 + (2sqrt3)^2 = 0
(x+2)^2 = -(2sqrt3)^2
x + 2 = +/- (2sqrt3)i
x = -2 +/- 2sqrt3 i

these are the roots...
4 , -2 + 2sqrt3 i , -2 - 2sqrt3 i ... §

Answer 2

You can use polar form to work this

3 roots; the solutions are 120° from each other

4, -2 + 2i√(3), -2 - 2i√(3) are the 3 solutions

You can check by cubing each answer; you will get 64

The factoring method is easier for this problem
x³ - 64 = 0
(x - 4)(x² + 4x + 16) = 0

x - 4 = 0 gives 4 as the answer

Using the quadratic formula for x² + 4x + 16 = 0
will give the other 2 answers -2 ± 2i√(3)

Answer 3

All 3 of them are 4.