Discussion:
unsolved
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spiny urchin
2015-05-09 20:00:34 UTC
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Here is attempted the intersection of a curve
f(x)=-10-2*x+2*(x^2)-x^3+2*(x^4) with the x-axis:

http://www.stonetabernacle.com/intersect-curve.html

(unsolved)

I am aware of Newton's Method, but it is useless when no close approximation
is able to be deduced.
Bill
2015-05-09 20:56:48 UTC
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Post by spiny urchin
Here is attempted the intersection of a curve
Clearly it has at least 2 real solutions by the Intermediate Value
Theorem. Apply a little Calculus and see is there is more than 1
relative min/max. Construct a nice graph.
Post by spiny urchin
http://www.stonetabernacle.com/intersect-curve.html
(unsolved)
I am aware of Newton's Method, but it is useless when no close
approximation is able to be deduced.
Samuel W. Flint
2015-05-10 03:29:13 UTC
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Or stick it into a CAS.

Maxima output follows:

sqrt(597811) 1403 1/6
147 (------------ + ----)
3/2 216
8 3 sqrt(597811) 1403 1/3 121 29
sqrt(- ------------------------------------------------------------------------ - (------------ + ----) + --------------------------- - --)
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3 3/2 216 sqrt(597811) 1403 1/3 24
8 sqrt(144 (------------ + ----) - 87 (------------ + ----) - 968) 8 3 18 (------------ + ----)
3/2 216 3/2 216 3/2 216
8 3 8 3 8 3
(%o1) [x = - ----------------------------------------------------------------------------------------------------------------------------------------------
2
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3
sqrt(144 (------------ + ----) - 87 (------------ + ----) - 968)
3/2 216 3/2 216
8 3 8 3 1
- ---------------------------------------------------------------------- + -, x =
sqrt(597811) 1403 1/6 8
24 (------------ + ----)
3/2 216
8 3
sqrt(597811) 1403 1/6
147 (------------ + ----)
3/2 216
8 3 sqrt(597811) 1403 1/3 121 29
sqrt(- ------------------------------------------------------------------------ - (------------ + ----) + --------------------------- - --)
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3 3/2 216 sqrt(597811) 1403 1/3 24
8 sqrt(144 (------------ + ----) - 87 (------------ + ----) - 968) 8 3 18 (------------ + ----)
3/2 216 3/2 216 3/2 216
8 3 8 3 8 3
----------------------------------------------------------------------------------------------------------------------------------------------
2
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3
sqrt(144 (------------ + ----) - 87 (------------ + ----) - 968)
3/2 216 3/2 216
8 3 8 3 1
- ---------------------------------------------------------------------- + -, x =
sqrt(597811) 1403 1/6 8
24 (------------ + ----)
3/2 216
8 3
sqrt(597811) 1403 1/6
147 (------------ + ----)
3/2 216
8 3 sqrt(597811) 1403 1/3 121 29
sqrt(------------------------------------------------------------------------ - (------------ + ----) + --------------------------- - --)
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3 3/2 216 sqrt(597811) 1403 1/3 24
8 sqrt(144 (------------ + ----) - 87 (------------ + ----) - 968) 8 3 18 (------------ + ----)
3/2 216 3/2 216 3/2 216
8 3 8 3 8 3
- --------------------------------------------------------------------------------------------------------------------------------------------
2
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3
sqrt(144 (------------ + ----) - 87 (------------ + ----) - 968)
3/2 216 3/2 216
8 3 8 3 1
+ ---------------------------------------------------------------------- + -, x =
sqrt(597811) 1403 1/6 8
24 (------------ + ----)
3/2 216
8 3
sqrt(597811) 1403 1/6
147 (------------ + ----)
3/2 216
8 3 sqrt(597811) 1403 1/3 121 29
sqrt(------------------------------------------------------------------------ - (------------ + ----) + --------------------------- - --)
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3 3/2 216 sqrt(597811) 1403 1/3 24
8 sqrt(144 (------------ + ----) - 87 (------------ + ----) - 968) 8 3 18 (------------ + ----)
3/2 216 3/2 216 3/2 216
8 3 8 3 8 3
--------------------------------------------------------------------------------------------------------------------------------------------
2
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3
sqrt(144 (------------ + ----) - 87 (------------ + ----) - 968)
3/2 216 3/2 216
8 3 8 3 1
+ ---------------------------------------------------------------------- + -]
sqrt(597811) 1403 1/6 8
24 (------------ + ----)
3/2 216
8 3

--
Samuel W. Flint
4096R/266596F4
(9477 D23E 389E 40C5 2F10 DE19 68E5 318E 2665 96F4)
(λs.(s s) λs.(s s))
spiny urchin
2015-05-13 06:54:19 UTC
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Post by Samuel W. Flint
Or stick it into a CAS.
sqrt(597811) 1403 1/6
147 (------------ + ----)
3/2 216
8 3
sqrt(597811) 1403 1/3 121 29
sqrt(- ------------------------------------------------------------------------
- (------------ + ----) + --------------------------- - --)
sqrt(597811) 1403 2/3 sqrt(597811)
1403 1/3 3/2 216 sqrt(597811) 1403 1/3
24
8 sqrt(144 (------------ + ----) - 87 (------------
+ ----) - 968) 8 3 18 (------------ + ----)
3/2 216 3/2
216 3/2 216
8 3 8 3
8 3
(%o1) [x
= - ----------------------------------------------------------------------------------------------------------------------------------------------
2
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3
sqrt(144 (------------ + ----) - 87 (------------ + ----) - 968)
3/2 216 3/2 216
8 3 8 3
1
- ---------------------------------------------------------------------- + -, x =
sqrt(597811) 1403 1/6
8
24 (------------ + ----)
3/2 216
8 3
sqrt(597811) 1403 1/6
147 (------------ + ----)
3/2 216
8 3
sqrt(597811) 1403 1/3 121 29
sqrt(- ------------------------------------------------------------------------
- (------------ + ----) + --------------------------- - --)
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3
3/2 216 sqrt(597811) 1403 1/3 24
8 sqrt(144 (------------ + ----) - 87 (------------ + ----) -
968) 8 3 18 (------------ + ----)
3/2 216 3/2 216
3/2 216
8 3 8 3
8 3
----------------------------------------------------------------------------------------------------------------------------------------------
2
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3
sqrt(144 (------------ + ----) - 87 (------------ + ----) - 968)
3/2 216 3/2 216
8 3 8 3
1
- ---------------------------------------------------------------------- + -, x =
sqrt(597811) 1403 1/6
8
24 (------------ + ----)
3/2 216
8 3
sqrt(597811) 1403 1/6
147 (------------ + ----)
3/2 216
8 3
sqrt(597811) 1403 1/3 121 29
sqrt(------------------------------------------------------------------------
- (------------ + ----) + --------------------------- - --)
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3
3/2 216 sqrt(597811) 1403 1/3 24
8 sqrt(144 (------------ + ----) - 87 (------------ + ----) -
968) 8 3 18 (------------ + ----)
3/2 216 3/2 216
3/2 216
8 3 8 3
8 3
- --------------------------------------------------------------------------------------------------------------------------------------------
2
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3
sqrt(144 (------------ + ----) - 87 (------------ + ----) - 968)
3/2 216 3/2 216
8 3 8 3
1
+ ---------------------------------------------------------------------- + -, x =
sqrt(597811) 1403 1/6
8
24 (------------ + ----)
3/2 216
8 3
sqrt(597811) 1403 1/6
147 (------------ + ----)
3/2 216
8 3
sqrt(597811) 1403 1/3 121 29
sqrt(------------------------------------------------------------------------
- (------------ + ----) + --------------------------- - --)
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3
3/2 216 sqrt(597811) 1403 1/3 24
8 sqrt(144 (------------ + ----) - 87 (------------ + ----) -
968) 8 3 18 (------------ + ----)
3/2 216 3/2 216
3/2 216
8 3 8 3
8 3
--------------------------------------------------------------------------------------------------------------------------------------------
2
sqrt(597811) 1403 2/3 sqrt(597811) 1403 1/3
sqrt(144 (------------ + ----) - 87 (------------ + ----) - 968)
3/2 216 3/2 216
8 3 8 3
1
+ ---------------------------------------------------------------------- + -]
sqrt(597811) 1403 1/6
8
24 (------------ + ----)
3/2 216
8 3
--
Samuel W. Flint
4096R/266596F4
(9477 D23E 389E 40C5 2F10 DE19 68E5 318E 2665 96F4)
(λs.(s s) λs.(s s))
I am looking for the general solution for any equation, something like
you've got but numbers replaced with variables.

Here I have added to the web page, though still without a solution:

http://www.stonetabernacle.com/intersect-curve.html

Thank you for your attention to this question!

Jon G.
Charlie Roberts
2015-05-14 12:33:32 UTC
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On Wed, 13 May 2015 02:54:19 -0400, "spiny urchin"
Post by spiny urchin
I am looking for the general solution for any equation, something like
you've got but numbers replaced with variables.
http://www.stonetabernacle.com/intersect-curve.html
Thank you for your attention to this question!
Jon G.
I have little idea of what you really want, but it appears
that you want to solve a quartic.

Check out

http://en.wikipedia.org/wiki/Quartic_function

for a start.

Good luck.

Charlie R
Samuel W. Flint
2015-05-14 20:30:27 UTC
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"spiny urchin" <***@nowhere.com> writes:


[...]
Post by spiny urchin
I am looking for the general solution for any equation, something like
you've got but numbers replaced with variables.
I guess that wasn't clear to me, sorry.
Post by spiny urchin
http://www.stonetabernacle.com/intersect-curve.html
Thank you for your attention to this question!
You are welcome.
Post by spiny urchin
Jon G.
Sam
--
Samuel W. Flint
4096R/266596F4
(9477 D23E 389E 40C5 2F10 DE19 68E5 318E 2665 96F4)
(λs.(s s) λs.(s s))
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