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

Question 700270: x^4=1
how do you solve this
Found 3 solutions by mananth, solver91311, MathLover1:
Answer by mananth(16949)   (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)   (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

Answer by MathLover1(20855)   (Show Source): You can put this solution on YOUR website!
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