Solving non-rational expressions on 49G?

[Nicolai Sten]

Hi.. Anyone knows how to solve these kinds of expressions on a HP49:?

((40000*A+4000)/exp(A))=5000

Looks very simple, but just get the words:
"Not reducible to a rational expression"

[Arnaud Amiel]

I wouldn't even know how to solve this by hand but the numeric solver [RS][7] gives the following answer straight away A=2.863E-2

You can also use ROOT which gives the same answer with a guess of 0. But a different answer with a guess of 2. So I don't know...

Arnaud

Edited: 16 June 2008, 10:01 a.m.

[Gerson W. Barbosa]

Quote:

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I wouldn't even know how to solve this by hand

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Neither would I, but I have researched and have found the exact result is

x = -W(-e^(-1/10)/8) - 1/10 or

x = 0.028630541938, to 12 places.

where W(x) is [link:http://en.wikipedia.org/wiki/Lambert's_W_function]Lambert's W function[/link]. Please take a look at the general solution formula in example 1. I think this matches the numeric result you have found.

Programs to compute the W function on the HP-33S and some other HP calculators can be found

here.

Regards,

Gerson.

[Jean-Michel]

Welcome back here, Gerson! (And congrats for your solution).
Regards

Jean-Michel.

[Arnaud Amiel]

Nice link. Spot on. Time to get back to do a bit of maths...

[Nicolai Sten]

Quote:

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I wouldn't even know how to solve this by hand ...

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That<'s what we have calculators for :)

I have just found out, thx to the numeric solver as you told me.

Thanks

[Karl Schneider]

Equation to solve, using the HP-49:

((40000*A+4000)/exp(A))=5000

which simplifies to

40*A - 5*exp(A) + 4 = 0

whose derivative is

40 - 5*exp(A)

Solving that for zero yields A = ln(8) ~= 2.079441542.

This is the inflection point for the initial guess that determines which solution the HP-15C gives, but not on the HP-49G.

Quote:

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the numeric solver [RS][7] gives the following answer straight away A=2.863E-2

You can also use ROOT which gives the same answer with a guess of 0. But a different answer with a guess of 2.

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The "different" (but still valid) answer is 3.30455610804.

My difficutly was figuring out how to copy 'n' paste the expression into the "NUM.SLV" form after symbolic solution "S.SLV" failed. I finally saved it to a variable and loaded that using "CHOOSE".

(Sigh.) Once again, I would have had my answers so much faster with an ancient HP-34C or HP-15C, despite the vast difference in computational speed.

-- KS

Edited: 17 June 2008, 1:56 a.m.