solve: y^4-16=0

Question

solve: y^4-16=0

amistre64 · Answer

y^4 = 16

2.2.2.2 = 4.4 = 16

-2.-2.-2.-2 = 4.4 = 16

anonymous · Answer

O.k I see that, so my answers should be 2, 2, -2, -2 right?

anonymous · Answer

difference of squares

anonymous · Answer

but I also see a difference of squares...

amistre64 · Answer

2 or -2 are the answer :)

anonymous · Answer

so there can be a complex solution as well.....

amistre64 · Answer

you want to solve for y?  or factor it?

amistre64 · Answer

all real numbers have 0i as a comlex part

anonymous · Answer

solve for y

amistre64 · Answer

since there are no 4rt(...) to worry about, you dont need to include and 0i parts

anonymous · Answer

thing is that I am trying to find the solution to a general differential equation..

amistre64 · Answer

y^4 = -16  has complex roots

amistre64 · Answer

then you should ask what it is your wanting to figure out lol

anonymous · Answer

+2i and -2i are also the roots.

anonymous · Answer

so the problem is y^4-16y=0

amistre64 · Answer

...... maybe :)

anonymous · Answer

at first i just found the +and - 2 as a multiple of four

anonymous · Answer

but then I saw the difference of squares and thought, o.k there are complex numbers so its gonna be different

amistre64 · Answer

(2i)^4 = 16.i^2.i^2 = 16  i tend to get lost with that

anonymous · Answer

so i first got y(x)= c1e^(2x)+c2xe^2x+c3x^2e^2x+c4x^3e^2x

anonymous · Answer

what grade are you in

anonymous · Answer

but if i take the complex numbers, then I would get y(x) = c1e^2x + c2e^2x + c3cos 2x + c4sin 2x

anonymous · Answer

Im a sophomore in college.

anonymous · Answer

do you know how to factor a difference of squares?

anonymous · Answer

yeah, I was just wondering if I would to take the Nth root how the question is then I would get +and -2 as a multiple of 4, but at the same time if I do the difference of squares then I will get complex numbers. Ijust want to understand if both answers would be right.

anonymous · Answer

I think since the questions asks to find the general solution to the differential equation, you have to include the complex number as part of your solution

anonymous · Answer

well I will just factor first before I try to solve, that way I can find all the solutions. Thanks for the help though.

anonymous · Answer

welcome...sounds great!

anonymous · Answer

you would still get same thing...2, -2, -2i, 2i