Solution to a Pentic

[Jon]

Solution to a pentic:

http://jons-math.bravehost.com/penticsoln.html

This shows the steps to derive the formula below.

The root to ax^5+bx+c=0 is,

x = { -c*({a^2+b^2}^(1/2)+a)/(b^2+a*{a^2+b^2}^(1/2)) }^(1/5)

Using this formula, the roots to,

x^5+x-34=0 x=1.888 should be 2
32x^5+4x-3=0 x=0.623 should be 1/2
x^5+x-0.10001 x=0.5887 should be 1/10

[Peter Webb]

Post by Jon
http://jons-math.bravehost.com/penticsoln.html
This shows the steps to derive the formula below.
The root to ax^5+bx+c=0 is,
x = { -c*({a^2+b^2}^(1/2)+a)/(b^2+a*{a^2+b^2}^(1/2)) }^(1/5)
Using this formula, the roots to,
x^5+x-34=0 x=1.888 should be 2
32x^5+4x-3=0 x=0.623 should be 1/2
x^5+x-0.10001 x=0.5887 should be 1/10

So the formula must be wrong.

Don't believe everything you read on the internet.

[Frank J. Lhota]

A quick question: are you familiar with Galois theory? If not, please
check out

http://www.galois-group.net/theory/math594fS.pdf

And if you are familiar with Galois theory, you really should identify
the error Évariste Galois made in his theory that has gone unnoticed for
nearly two centuries.
--
"All things extant in this world,
Gods of Heaven, gods of Earth,
Let everything be as it should be;
Thus shall it be!"
- Magical chant from "Magical Shopping Arcade Abenobashi"

"Drizzle, Drazzle, Drozzle, Drome,
Time for this one to come home!"
- Mr. Wizard from "Tooter Turtle"