SOLUTION: Solve the following equation in the complex number system 1.X^3 - 8 = 0 2. X^3 + 27 = 0 my solution 1. X^3

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Question 10848: Solve the following equation in the complex number system

1.X^3 - 8 = 0
2. X^3 + 27 = 0

my solution
1. X^3 - 8 = 0
X^3 = 8
X= 3root 8
X= +- 2
X= +2 , -2

2. X^3 + 27 = 0
x^3=27
X =+- 3root 27
X= + - 3
X= =3, -3
I know I'm wrong but I don't know why. kindly help.
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
1) Add 8 to both sides, which you did already.
Take the cube root of both sides.

-2 is not a root since: = -8
2) Subtract 27 from both sides.
Take the cube root of both sides.

+3 is not a root since: = +27
Please ignore the above...it's wrong!
1) This is the difference of two cubes which can be factored as follows:

, so One root.
Use the quadratic formula:

or The other two roots.
2) This is the sum of two cubes which can be factored as follows:
Setting each factor = 0.

This is one of the roots.
Use the quadratic formula:

or The other two roots.
These can also be written:
and

SOLUTION: Solve the following equation in the complex number system 1.X^3 - 8 = 0 2. X^3 + 27 = 0 my solution 1. X^3 - 8 = 0 X^3 = 8 X= 3root 8 X= +- 2