SOLUTION: x^4=1 how do you solve this

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Question 700270: x^4=1
how do you solve this
Found 3 solutions by mananth, solver91311, MathLover1:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
x^4=1
x^4-1=0
(x^2+1)(x^2-1)=0
(x^2+1)(x+1)(x-1)=0
If (x^2+1)=0
x^2=-1
x= sqrt(-1)=i
OR x= -1 OR +1

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Rearrange



Let

Substitute



Factor the difference of two squares



Therefore



or



But







or



and





So



In summary:



or



Fulfilling the requirement of the Fundamental Theorem of Algebra that says that a 4th degree polynomial equation must have 4 roots.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4=1...=>...x=root%284%2C1%29...=>...x=1 or x=-1...real solutions and x=i or x=-i...complex solutions

check solutions:
if x=1...=>.. 1%5E4=1....=>.. 1%2A1%2A1%2A1=1...=>...1=1...true
if x=%28-1%29...=>.. %28-1%29%5E4=1....=>.. %28-1%29%2A%28-1%29%2A%28-1%29%2A%28-1%29=1...=>...1=1...true
if x=i...=>.. i%5E4=1....=>.. i%2Ai%2Ai%2Ai=1...=>...i%5E2%2Ai%5E2=1.....=>...%28-1%29%2A%28-1%29=1...=>...1=1...true
if x=%28-i%29...=>.. %28-i%29%5E4=1....=>.. %28-i%29%2A%28-i%29%2A%28-i%29%2A%28-i%29=1...=>...%28-i%29%5E2%2A%28-i%29%5E2=1......=>...%28-1%29%2A%28-1%29=1...=>...1=1..true