Hello.
I have been stuck on these two problems forever.
Find all four roots of the equation:
x4-2x2+4 = 0
As far as I know the only way to find an answer here is by factoring, but I can't seem to figure it out.
I don't know all the rules when factoring with complex numbers.
One of my failed attempts looked like this: (x2-1+i)(x2+1+i), (didn't go further).
The other problem:
Evaluate the limit:
lim |x-4|-2
x->2 (x-2)
Does this not exist? I tried multiplying with (x+2), but it didn't get me anywhere.
I also tried approaching 2 from both sides. I remember an example in my calculus book where the denominator looked like this(absolute value in numerator): (x-2)(x+3). When approaching 2 from left, or right, this didn't result in 0(2+3), but rather a positive or negative outcome. Can I do the same here? And if not, why?
Any help would be appreciated
I have been stuck on these two problems forever.
Find all four roots of the equation:
x4-2x2+4 = 0
As far as I know the only way to find an answer here is by factoring, but I can't seem to figure it out.
I don't know all the rules when factoring with complex numbers.
One of my failed attempts looked like this: (x2-1+i)(x2+1+i), (didn't go further).
The other problem:
Evaluate the limit:
lim |x-4|-2
x->2 (x-2)
Does this not exist? I tried multiplying with (x+2), but it didn't get me anywhere.
I also tried approaching 2 from both sides. I remember an example in my calculus book where the denominator looked like this(absolute value in numerator): (x-2)(x+3). When approaching 2 from left, or right, this didn't result in 0(2+3), but rather a positive or negative outcome. Can I do the same here? And if not, why?
Any help would be appreciated