Answer:
Step-by-step explanation:
A difference of two perfect cubes, x^3 - y^3 can be factored into
(x-y) • (x^2 +xy +y^2) =0 equation 1
x ^3 - 64 = 0
(x)^3 - (4)^3 = 0 equation 2
Now substituting equation 2 into equation 1, we get
(x-4) (x^2+(x).(4) +(4)^2) = 0
(x-4) (x^2+4x+16) = 0
so the solutions are
1) x - 4 =0
x=4
x^2 + 4x + 16 = 0
By using the quadratic formula we get the followig solutions:
- B ± √ B2-4AC
x = ————————
2A
x =(-4-√-48)/2=-2-2i√ 3 = -2.0000-3.4641i
x =(-4+√-48)/2=-2+2i√ 3 = -2.0000+3.4641i
