Re: Mathematica issue

*To*: mathgroup at smc.vnet.net*Subject*: [mg127861] Re: Mathematica issue*From*: "Dr. Wolfgang Hintze" <weh at snafu.de>*Date*: Tue, 28 Aug 2012 04:50:22 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <k1epvg$rnq$1@smc.vnet.net>

On 27 Aug., 05:36, Matthias Bode <lvs... at hotmail.com> wrote: > Hola: > As neither Solve[] nor Reduce[] find an analytical solution there isn't any - most probably. > One might, however, do - inter alia - this: > Clear[a0, a1, b0, b1, c0, d0, eq01, sol01]eq01 = Expand[a0 + b0 + x^a1*(c0 - d0*x^b1) == 0]; sol01 = FindInstance[eq= 01, {a0, b0, c0, d0, a1, b1, x}, Reals]a0 + b0 + x^a1*(c0 - d0*x^b1) == 0 /. sol01N[sol01] > Out[3]= {{a0 -> (46314691670528 - 1684956133536* 134^(7/10) - 15*134^(4/5))/ 57893364588160, b0 -> -(4/5), c0 -> 39/10, d0 -> -(3/2), a1 -> -(3/10), b1 -> -(49/10), x -> 134}} > Out[4]= {True} > Out[5]= {{a0 -> -0.09729070208467958, b0 -> -0.8, c0 -> 3.9,d0 -> -1.5, a1 -> -0.3, b1 -> -4.9, x -> 134.}} > Best regards, > MATTHIAS BODE > S 17.35775=B0, W 066.14577=B0 > 2'740 m > AMSL. > > > > > > > From: n... at 12000.org > > Subject: Re: Mathematica issue > > To: mathgr... at smc.vnet.net > > Date: Sun, 26 Aug 2012 05:45:30 -0400 > > > On 8/26/2012 3:18 AM, Nasser M. Abbasi wrote: > > > >> I need analytical expression for the x in terms of A,B,C,D and a,b, > > > > try this: > > > > parms = {A0 -> 1, B0 -> 2, a -> 3, C0 -> 4, D0 -> 5, b -> 6} > > > eq = A0 + B0 + x^a (C0 - D0 x^b) == 0 > > > sol = Solve[eq /. parms, x] > > > Opps, just noticed you want symbolic solution. > > Mathematica 8.04 does not do it. I doubt this can be solved symbolicall= y. > > Need to use some numbers for the parameters. > > > Clear[A0, B0, a , C0, D0 , b] > > eq = A0 + B0 + x^a (C0 - D0 x^b) == 0 > > Solve[eq, x] > > > Solve::nsmet: This system cannot be solved with the methods available t= o = > Solve. >> > > > --Nasser If you restrict yourself to integer exponents, the solubility of the equation is governed by the Abel=96Ruffini theorem: In algebra, the Abel=96Ruffini theorem (also known as Abel's impossibility theorem) states that there is no general algebraic solution=97that is, solution in radicals=97 to polynomial equations of degree five or higher. You might want to watch this in Mathematica usind this command Table[{n, eq = x^n + a*x + b == 0; Simplify[Solve[eq, x]]}, {n, 1, 5}] More generally you are facing a transcendental quation which has no closed solution in most cases but must be soved numerically. Here's an example: In[57]:= eq1 = x^(-E) + x^Pi == 3 Out[57]= x^(-E) + x^Pi == 3 Watch the behaviour of the function In[66]:= Plot[{3, x^(-E) + x^Pi}, {x, 0, 2}] [... the graph of the function] and then find the solutions (roots) numerically In[61]:= FindRoot[eq1, {x, 1}] Out[61]= {x -> 1.34813204709293} In[62]:= FindRoot[eq1, {x, 0.5}] Out[62]= {x -> 0.6958252736289695} Regards, Wolfgang