SOLUTION: find all solutions, real and complex, of the equation. show all work. x^6-65x^3+64=0

Algebra ->  Trigonometry-basics -> SOLUTION: find all solutions, real and complex, of the equation. show all work. x^6-65x^3+64=0      Log On


   

Question 422941: find all solutions, real and complex, of the equation. show all work.
x^6-65x^3+64=0
Answer by shree840(260) About Me  (Show Source):
You can put this solution on YOUR website!
Let x3 be y
y2-65y+64=0
y^2-64y-y+64=0
y(y-64)-1(y-64)=0
(y-1)(y-64)=0
solutions y-1=0 or y=1 or X^3=1 or x=1
y-64=0
y=64
x^3=64
x=4
Note because it is cube , you do not have + and -
The sign remains the same