SOLUTION: Using the square root method how do I solve x^4-16=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Using the square root method how do I solve x^4-16=0      Log On


   

Question 852097: Using the square root method how do I solve
x^4-16=0
Found 2 solutions by Alan3354, Boston_Don:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Using the square root method how do I solve
x^4-16=0
-------------
x%5E4+=+16
x%5E2+=+4
x = -2, 2
---------------
x%5E2+=+-4
x = -2i, 2i

Answer by Boston_Don(1) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4-16=0
x%5E4=16
sqrt%28x%5E4%29=sqrt%2816%29
x%5E2=4
sqrt%28x%5E2%29=sqrt%284%29
x=2
But we also have to consider the negative and imaginary solutions as well.
The former gives us
X=2, -2
For the latter i%5E2=-1 and hence i%5E4=%28i%5E2%29%5E2=1 .
This gives us the following two additional solutions
X=2i, -2i