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So I was working on a little project the other day and it was in regards to the cubic formula...

Which can be found here:

http://en.wikipedia.org/wiki/Cubic_formula#General_formula_of_roots

basically given an equation of the form:

ax^{3}+ bx^{2}+ cx + d = 0 the formulas on the attached link will give you the three values of x that satisfy this equation.

Here is my dilemma,

I was just kind of playing around with the quadratic equation which is:

x = [itex]\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/itex]

It can be conveniently "re arranged" to look like this:

(2ax + b)^{2}= b^{2}- 4ac

So in dealing with the cubic equation I tried the same thing which was fairly simple:

(3ax + b) = Ω (where Ω is all of our other business that remains)...

Can somebody tell me the simplified value of Ω^{3}?

Its terribly difficult to solve by hand and I do not own a symbolic calculator can manipulate it so if somebody could do the solution that would be convenient...

Additionally I would like to know another value:

Ω can be seen as the sum of (σ + μ) (see the two giant cube roots in the wiki article, those are sig and mu for this expression).

What is (σ^{2}- σμ + μ^{2})?

and What is (σ^{3}- μ^{3})

Hopefully between those three questions I can resolve to find a pattern between the quadratic and cubic formulas.

Thanks!

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# Cubing the Cubic Formula Help would be greatly appreciated

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