Re: y^3 -y + 1/8 = 0 Some intellectual muscle sought here

From: Eduardo <abdulai@xxxxxxxxxxx>
Date: Thu, 05 Jul 2007 11:29:08 -0700

On Jul 4, 8:43 pm, rachel.c...@xxxxxxxxxxx wrote:

A very interesting equation and question has been brough to my
attention by our students:-

y^3 -y + 1/8 = 0

Concerning this equation the solutions to which the author is well
aware of :-

y= 0.93040292655585
y= -1.05745377073838
y= 0.12705084418253

his/her question is whether there is a Hyperbolic Tanh way of arriving
at these solutions.

Specifically what the author says is
"Can any person make a step-by-step proof that is easy to follow
showing why this is impossible or not"

Can anyone help me and by extension him/her throw light on this.

I mean really help and not to be issuing effortless academic fatwas
that do not in any way lend themselves to a solution.

At the time of writing there is but one reply that seems to ignore the
intent of the question suggesting a well known Sinh(3?)/Sinh(?)
relationship.

In the absence of any proofing or testing with the above verified non-
complex solutions the respondent makes use of words such as 'Always
may be EASILY solved' and '(obviously, you MUST use complex numbers)'.

The expression without complex numbers was posted before.

Rachel, what you really need is a cavernous muscle.

I think this equation would prove very interesting to young students
learning to reason and discern from first principles rather than from
generalisations decreed with cavalier dogmatism.

Would anyone capable of doing justice to the question help us out
here?

Rachel Coen

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