How to solve non-rational expression on HP49...?
in [HP48]
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From: Nicolai Sten on 16 Jun 2008 07:59 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" I know that TI-89's can do the job, but what is the trick on HP49?
From: Bill Markwick on 16 Jun 2008 09:49 On Jun 16, 7:59 am, Nicolai Sten <nicolai_s...(a)hotmail.com> wrote: > Hi.. Anyone knows how to solve these kinds of expressions on a HP49:? > > ((40000*A+4000)/exp(A))=5000 > Sometimes the symbolic solver digs in its irrational heels. A way around it is to store the equation in EQ and select RS-NUM.SLV and then Solve Equation. It gave the answer 2.86305419388E-2 for A in about one second. Bill
From: Arnaud Amiel on 16 Jun 2008 10:59 On Jun 16, 2:49 pm, Bill Markwick <bd...(a)torfree.net> wrote: > On Jun 16, 7:59 am, Nicolai Sten <nicolai_s...(a)hotmail.com> wrote: > > > Hi.. Anyone knows how to solve these kinds of expressions on a HP49:? > > > ((40000*A+4000)/exp(A))=5000 > > Sometimes the symbolic solver digs in its irrational heels. A way > around it is to store the equation in EQ and select RS-NUM.SLV and > then Solve Equation. It gave the answer 2.86305419388E-2 for A in > about one second. > > Bill This is one of the Solutions. If you do 'EQ' [ENTER] 'A' [ENTER] 3 [ENTER] ROOT [ENTER] you should get the other one around 3.30. I seriously doubt the TI89 would be able to solve this symbolicly though. If it does, I would be interested in the answer Arnaud
From: sc_usenet on 16 Jun 2008 11:52 On Jun 16, 10:59 am, Arnaud Amiel <aam...(a)gmail.com> wrote: > > I seriously doubt the TI89 would be able to solve this symbolicly > though. If it does, I would be interested in the answer > > Arnaud It can't. On my emulator, the TI89 returns two solutions: A = 3.304..., A = 0.02863... . It just appears that the TI89 automatically switches to numeric mode when an equation can't be solved symbolically. It also insists on searching for "all" possible solutions, and it's fun to trick with some periodic function such as SIN(X) = EXP(X). S.C.
From: Scott Hemphill on 16 Jun 2008 13:40
Arnaud Amiel <aamiel(a)gmail.com> writes: > On Jun 16, 2:49 pm, Bill Markwick <bd...(a)torfree.net> wrote: >> On Jun 16, 7:59 am, Nicolai Sten <nicolai_s...(a)hotmail.com> wrote: >> >> > Hi.. Anyone knows how to solve these kinds of expressions on a HP49:? >> >> > ((40000*A+4000)/exp(A))=5000 >> >> Sometimes the symbolic solver digs in its irrational heels. A way >> around it is to store the equation in EQ and select RS-NUM.SLV and >> then Solve Equation. It gave the answer 2.86305419388E-2 for A in >> about one second. >> >> Bill > > This is one of the Solutions. If you do 'EQ' [ENTER] 'A' [ENTER] 3 > [ENTER] ROOT [ENTER] you should get the other one around 3.30. > > I seriously doubt the TI89 would be able to solve this symbolicly > though. If it does, I would be interested in the answer Mathematica solves this symbolicly, using the function ProductLog. ProductLog[z] gives the principal solution for w in z = w e^w. ProductLog[k, z] gives the kth solution. In[1]:= a /. Solve[(40000*a+4000)/Exp[a] == 5000] InverseFunction::ifun: Inverse functions are being used. Values may be lost for multivalued inverses. Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. -1 -1 -1 - 10 ProductLog[-------] -1 - 10 ProductLog[-1, -------] 1/10 1/10 8 E 8 E Out[1]= {---------------------------, -------------------------------} 10 10 In[2]:= N[%,32] Out[2]= {0.028630541938670887478223773529550, > 3.3045561080359331964430691736005} If you use "Reduce" as the warning suggests, you can find an infinite number of complex solutions, as well. Scott -- Scott Hemphill hemphill(a)alumni.caltech.edu "This isn't flying. This is falling, with style." -- Buzz Lightyear |