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Math Help - Difference of cubes

  1. #1
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    Difference of cubes

    Find all solutions of the following equation. (If there are more answer boxes than answers, enter NONE in the extra boxes.) a3x3 + 1000 = 0
    x = 1
    (real solution)
    x = 2
    (smaller imaginary part)
    x = 3
    (larger
    I was able to figure out part one and for 2 and 3 this is what i came up with but they are incorrect.
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  2. #2
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    Quote Originally Posted by tmac11522 View Post
    Find all solutions of the following equation. (If there are more answer boxes than answers, enter NONE in the extra boxes.) a3x3 + 1000 = 0
    x = 1
    (real solution)
    x = 2
    (smaller imaginary part)
    x = 3
    (larger
    I was able to figure out part one and for 2 and 3 this is what i came up with but they are incorrect.
    The last two cannot be solutions as they contain x.

    .
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by tmac11522 View Post
    Find all solutions of the following equation. (If there are more answer boxes than answers, enter NONE in the extra boxes.) a3x3 + 1000 = 0
    x = 1
    (real solution)
    x = 2
    (smaller imaginary part)
    x = 3
    (larger
    I was able to figure out part one and for 2 and 3 this is what i came up with but they are incorrect.
    ditto to what Constantine said

    i assume by a3x3 you mean a^3x^3 ??

    in that case, note that what you have is:

    (ax)^3 + 10^3 = 0

    you can use the sum of two cubes formula: n^3 + m^3 = (n + m)(n^2 - nm + m^2)

    the first factor gave you the first solution. use the quadratic formula on the second factor to get the second solution. here your n = ax and your m = 10
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