why the FUCK are polynomials of deg>4 IMPOSSIBLE to solve

they're not

x^4-1 is easy

>>9154959
I mean in general you pea-brain

>IMPOSSIBLE to solve
[math]x^5=-1[/math]

>>9154965
I mean in general you double pea-brain

>>9154963
>I mean in general you pea-brain
then because of abel's theorem
http://www.maths.ed.ac.uk/~aar/papers/abel.pdf

File: Capture.png (145KB, 267x391px) Image search: [Google]

145KB, 267x391px

>>9154970

>>9154955
what do you mean by algebraically? quintics are solvable in terms of radicals and ultraradicals

>>9154963
>>9154968
>I mean
>I mean
>I don't know WTF I mean
you quintic pea-brain

>>9154978

An algebraic solution only employs three basic (mostly*) binary operations and their inverses, to the exclusion of other sorts of operations:

+-, x/, ^√.

That is what is meant by /algebraic solution/ -appropriate expressions, equations etc only employing the above six operations.

As other anons have correctly observed ITT, there are specific quintics, sextics etc for which such above algebraic solutions may be found, but this is distinct from what Abel-Ruffini is all about, which is to establish that such-and-such /general/ algebraic solutions for the /general/ such-and-such quintic, sextic, etc, may not be obtained /as algebraic solutions as-such/. This is where ultraradicals step in, and so step outside of the above restriction, so that Abel-Ruffini still holds in its own sphere, as it were, while more sophisticated stuff can be brought to bear on the quintic. That such stuff can be done doesn't at all obviate Abel-Ruffini though, which is the point.

Isn't it that for SOME polynomials of degree more than 4 you can only ever approximate a solution, there is no general formula. Proof? wolfram does'nt offer exact roots for some polynomials...

>>9155172
>Isn't it that for SOME polynomials of degree more than 4 you can only ever approximate a solution, there is no general formula.
no
https://en.wikipedia.org/wiki/Quartic_function#Solving_a_quartic_equation

>>9155172

You're getting close. read the statement of abel-ruffini as given at wiki.

>>9154959
X^5 = 1

[math] \mathbb{G} \mathbb{A} \mathbb{L} \mathbb{O} \mathbb{I} \mathbb{S}[/math]

[math] \mathbb{T} \mathbb{H} \mathbb{E} \mathbb{O} \mathbb{R} \mathbb{Y}[/math]

>>9154970
oh, it's not soluble. of course. facepalm.

If polynomials with dregree bigger than 3 are unsolvable then how does Wolfram Mathematica solves them?

It's actually a conspiracy on the part of (((them))). They'll tell you how to solve it for a price

>>9154955
Because of the Jews.