- #1
Frogeyedpeas
- 80
- 0
Hi,
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:
ax3 + bx2 + 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 = b2 - 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 Ω3?
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 (σ2 - σμ + μ2)?
and What is (σ3 - μ3)
Hopefully between those three questions I can resolve to find a pattern between the quadratic and cubic formulas.
Thanks!
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:
ax3 + bx2 + 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 = b2 - 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 Ω3?
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 (σ2 - σμ + μ2)?
and What is (σ3 - μ3)
Hopefully between those three questions I can resolve to find a pattern between the quadratic and cubic formulas.
Thanks!