SOLUTION: x^3=1 What are all real and complex solutions. I have the answer in my book but I don't understand where it came from.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: x^3=1 What are all real and complex solutions. I have the answer in my book but I don't understand where it came from.      Log On


   

Question 354980: x^3=1

What are all real and complex solutions. I have the answer in my book but I don't understand where it came from.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3=1 Start with the given equation.


x%5E3-1=0 Subtract 1 from both sides.


%28x-1%29%28x%5E2%2Bx%2B1%29=0 Factor the left side using the difference of cubes formula.


x-1=0 or x%5E2%2Bx%2B1=0 Use the zero product property.


Now solve x-1=0 to get x=1


Next, solve x%5E2%2Bx%2B1=0 to get x+=+%28-1%2Bi%2Asqrt%283%29%29%2F%282%29 or x+=+%28-1-i%2Asqrt%283%29%29%2F%282%29. See this page for the steps on solving x%5E2%2Bx%2B1=0


So the solutions are x=1, x+=+%28-1%2Bi%2Asqrt%283%29%29%2F%282%29 or x+=+%28-1-i%2Asqrt%283%29%29%2F%282%29


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim