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Math Help - Solving Cubic Equations

  1. #1
    Junior Member 22upon7's Avatar
    Joined
    Nov 2008
    Posts
    60

    Solving Cubic Equations

    Hi,

    Could you please explain how to solve these two sums, step by step please.

    1. 2x^3=16x
    2. 2(x-1)^3=32

    This is as far as I got on both sums:

    1.
    2x^3=16x
    x^3=8x
    x^2=8
    x^2-8=0

    2.
    2(x-1)^3=32
    (x-1)^3=16
    (x-1)^3-16=0

    Any help would be greatly appreciated,

    Thanks,

    Dru
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  2. #2
    Senior Member
    Joined
    Nov 2008
    Posts
    461
    Hi.

    Quote Originally Posted by 22upon7 View Post
    Hi,

    Could you please explain how to solve these two sums, step by step please.

    1. 2x^3=16x
    2. 2(x-1)^3=32

    This is as far as I got on both sums:

    1.
    2x^3=16x
    x^3=8x
    x^2=8
    x^2-8=0
    Good thinking, but you made a mistake

    x^3=8x

    OKAY

    x^2=8

    Not okay, you divided by x; you can do that, but this is only for x \not= 0; and x = 0 is a solution!

    So

    x^3=8x

    x^3-8x = 0

    x(x^2-8) = 0

    is better,

    now you know x = 0 is a solution and x-8 = 0 leads to the other solutions; you still have to solve x-8= 0, tho.


    Quote Originally Posted by 22upon7 View Post
    2.
    2(x-1)^3=32
    (x-1)^3=16
    (x-1)^3-16=0
    The last step seems to be unnecessary

    (x-1)^3=16 // ^(1/3)

    x-1 = 16^{1/3}

    x = 16^{1/3}+1

    Quote Originally Posted by 22upon7 View Post
    Any help would be greatly appreciated,

    Thanks,
    You're welcome.

    Yours, Rapha
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