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3a, add +b and then cube the entire thing?

  1. Mar 19, 2012 #1
    A quick question... what is the resultant expression if you multiply the cubic formula by 3a, add +b and then cube the entire thing?

    Much appreciated
     
  2. jcsd
  3. Mar 19, 2012 #2

    berkeman

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    Staff: Mentor

    Pi.

    Cool problem. Thanks.
     
  4. Mar 19, 2012 #3

    chiro

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    Science Advisor

    Aside from delicious pi, have you tried just writing the equation of a cubic polynomial down and then doing your operations using normal algebra?
     
  5. Mar 20, 2012 #4

    HallsofIvy

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    To clarify, what do you mean by "the cubic formula"? chiro seems to think you mean just a cubic polynomial. Is that correct?
     
  6. Mar 20, 2012 #5
    I'm trying to rewrite the cubic formula (the general solution for the roots of a cubic polynomial into the form (3ax +b)^3 = ...

    Where normally given a cubic polynomial equation

    ax^3 + bx^2 + cx + d = 0

    The answer can be found by making the substitution:

    a = b/a

    b = c/a

    c = d/a

    and then the formula is in this link:

    http://planetmath.org/encyclopedia/CubicFormula.html [Broken]
     
    Last edited by a moderator: May 5, 2017
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