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anonymous

  • 5 years ago

solve: y^4-16=0

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  1. amistre64
    • 5 years ago
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    y^4 = 16 2.2.2.2 = 4.4 = 16 -2.-2.-2.-2 = 4.4 = 16

  2. anonymous
    • 5 years ago
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    O.k I see that, so my answers should be 2, 2, -2, -2 right?

  3. anonymous
    • 5 years ago
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    difference of squares

  4. anonymous
    • 5 years ago
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    but I also see a difference of squares...

  5. amistre64
    • 5 years ago
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    2 or -2 are the answer :)

  6. anonymous
    • 5 years ago
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    so there can be a complex solution as well.....

  7. amistre64
    • 5 years ago
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    you want to solve for y? or factor it?

  8. amistre64
    • 5 years ago
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    all real numbers have 0i as a comlex part

  9. anonymous
    • 5 years ago
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    solve for y

  10. amistre64
    • 5 years ago
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    since there are no 4rt(...) to worry about, you dont need to include and 0i parts

  11. anonymous
    • 5 years ago
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    thing is that I am trying to find the solution to a general differential equation..

  12. amistre64
    • 5 years ago
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    y^4 = -16 has complex roots

  13. amistre64
    • 5 years ago
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    then you should ask what it is your wanting to figure out lol

  14. anonymous
    • 5 years ago
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    +2i and -2i are also the roots.

  15. anonymous
    • 5 years ago
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    so the problem is y^4-16y=0

  16. amistre64
    • 5 years ago
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    ...... maybe :)

  17. anonymous
    • 5 years ago
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    at first i just found the +and - 2 as a multiple of four

  18. anonymous
    • 5 years ago
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    but then I saw the difference of squares and thought, o.k there are complex numbers so its gonna be different

  19. amistre64
    • 5 years ago
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    (2i)^4 = 16.i^2.i^2 = 16 i tend to get lost with that

  20. anonymous
    • 5 years ago
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    so i first got y(x)= c1e^(2x)+c2xe^2x+c3x^2e^2x+c4x^3e^2x

  21. anonymous
    • 5 years ago
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    what grade are you in

  22. anonymous
    • 5 years ago
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    but if i take the complex numbers, then I would get y(x) = c1e^2x + c2e^2x + c3cos 2x + c4sin 2x

  23. anonymous
    • 5 years ago
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    Im a sophomore in college.

  24. anonymous
    • 5 years ago
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    do you know how to factor a difference of squares?

  25. anonymous
    • 5 years ago
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    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.

  26. anonymous
    • 5 years ago
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    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

  27. anonymous
    • 5 years ago
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    well I will just factor first before I try to solve, that way I can find all the solutions. Thanks for the help though.

  28. anonymous
    • 5 years ago
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    welcome...sounds great!

  29. anonymous
    • 5 years ago
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    you would still get same thing...2, -2, -2i, 2i

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