The Museum of HP Calculators

HP Forum Archive 18

 Solving non-rational expressions on 49G?Message #1 Posted by Nicolai Sten on 16 June 2008, 7:12 a.m. 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"

 Re: Solving non-rational expressions on 49G?Message #2 Posted by Arnaud Amiel on 16 June 2008, 9:57 a.m.,in response to message #1 by Nicolai Sten 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.

 Re: Solving non-rational expressions on 49G?Message #3 Posted by Gerson W. Barbosa on 16 June 2008, 12:16 p.m.,in response to message #2 by Arnaud Amiel Quote: I wouldn't even know how to solve this by hand 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.

 Re: Solving non-rational expressions on 49G?Message #4 Posted by Jean-Michel on 17 June 2008, 7:01 a.m.,in response to message #3 by Gerson W. Barbosa Welcome back here, Gerson! (And congrats for your solution). Regards Jean-Michel.

 Re: Solving non-rational expressions on 49G?Message #5 Posted by Arnaud Amiel on 18 June 2008, 6:13 a.m.,in response to message #3 by Gerson W. Barbosa Nice link. Spot on. Time to get back to do a bit of maths...

 Re: Solving non-rational expressions on 49G?Message #6 Posted by Nicolai Sten on 16 June 2008, 1:00 p.m.,in response to message #2 by Arnaud Amiel Quote: I wouldn't even know how to solve this by hand ... That<'s what we have calculators for :) I have just found out, thx to the numeric solver as you told me. Thanks

 Re: Solving non-rational expressions on 49G?Message #7 Posted by Karl Schneider on 17 June 2008, 1:30 a.m.,in response to message #2 by Arnaud Amiel 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: 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. 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.

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