Results 1 to 2 of 2

Math Help - Solution to Cubic

  1. #1
    Junior Member
    Joined
    Jun 2006
    Posts
    37

    Solution to Cubic

    Given that -
    3^1/3 + 3^-1/3 = x

    Prove that -
    3x^3 - 9x - 10 = 0



    Please help! PLEASE!

    My friend suggested something like taking 3^1/3 as 'a'.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Ruler of Hell View Post
    Given that -
    3^1/3 + 3^-1/3 = x

    Prove that -
    3x^3 - 9x - 10 = 0



    Please help! PLEASE!

    My friend suggested something like taking 3^1/3 as 'a'.
    Cube the first equation:

    x^3 = 3 + 3*3^{2/3}*3^{-1/3} + 3*3^{1/3}*3^{-2/3} + 1/3

    Now multiply through by 3:

    3*x^3 = 10 + 9*[3^{1/3} + 3^{-1/3}] = 10 + 9*x

    rearrange and:

    3x^3 - 9x - 10 = 0

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: September 23rd 2011, 03:39 AM
  2. Replies: 1
    Last Post: March 24th 2010, 12:14 AM
  3. Replies: 2
    Last Post: September 7th 2009, 02:01 PM
  4. Solution of Cubic
    Posted in the Algebra Forum
    Replies: 5
    Last Post: March 21st 2008, 03:26 AM
  5. My Cubic Solution
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 8th 2007, 07:08 AM

Search Tags


/mathhelpforum @mathhelpforum