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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

God
2006-01-09 08:41:47

I guess you might as well just use Newton's recursion for these things...

krassi_holmz
2006-01-09 04:30:07

That's why I prefer the approximated result.

God
2006-01-09 04:21:32

Lol.thanks... wow... that looks so complicated lol

krassi_holmz
2006-01-06 21:23:49

The general quintic can be solved in terms of Jacobi theta functions, as was first done by Hermite  in 1858. Kronecker  subsequently obtained the same solution more simply, and Brioschi also derived the equation.

krassi_holmz
2006-01-06 21:21:40

Yes, I've read very much about Abel.

And the Galous theory simplifies the result.
The solubility of an equation depends of the structude if its Galous group.

ganesh
2006-01-06 15:34:50

Very good posts and images uploaded, krassi_holmz. Those would be very useful. BTW, did you know the insolubility of the quintic equation was shown first by Neils Henrik Abel, the Norwegain Mathematician?

krassi_holmz
2006-01-05 21:25:50

this is the exact root!

krassi_holmz wrote:

For you question we get:

krisper
2006-01-05 21:16:31

I am sure you could find this without using the cubic formula.
x^3 - x - 1 = 0
x(x^2-1) = 1
if x = 0, the equasion has no meaning, so x must differ from 0 (x<>0); Now we can devide by x.
x^2 - 1 = 1/x.
We draw the graphics of these two expressions - x^2 - 1 and 1/x. After that we check where they cross eachother. This happens only in I quadrant which means that x^3 - x - 1 = 0 has only one real root. Afterwards doing some calculas we find that the root is somewhere between 1 and √2. Now we have to use the tangents and make some calculations and I am sure we will get the exact value of this root.

krassi_holmz
2006-01-05 21:13:30

Equations >4 are unsolvable exactin radicals. (Galoa)

krassi_holmz
2006-01-05 21:12:05

For you question we get:

krassi_holmz
2006-01-05 21:10:17

And quadric equation (useless):

krassi_holmz
2006-01-05 21:09:13

Cubic equation:

krassi_holmz
2006-01-05 21:07:58

The roots of quadratic equation ax^2+bx+c:

ganesh
2006-01-05 15:26:50

I did not know the roots of a cubic equation and looked for it on the net. I got to this pdf. Ricky, you can find the root of the incomplete cubic equation using the formulae.

Ricky
2006-01-05 09:33:23

If you use the cubic formula, shouldn't you come up with the exact root?

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