Re: Re: Re: Solve given that a variable is between 0 and 1
- To: mathgroup at smc.vnet.net
- Subject: [mg52683] Re: [mg52659] Re: [mg52636] Re: Solve given that a variable is between 0 and 1
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 9 Dec 2004 20:22:37 -0500 (EST)
- References: <200412070909.EAA09210@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
This is indeed the kind of problem that is not very suitable for a computer algebra program. But with a little human help Matheamtica can manage it (well, sort of ) eq1 = w - k^(1 - b)*r*((-((a*k^b - OverBar[y])/a))^(1/b))^ (-1 + b) == 0 rule = (a*k^b - OverBar[y])/a -> d Solve[PowerExpand[Eliminate[{Equal @@ rule, eq1 /. rule}, d]], k] ..... various messages ...... {{k -> ((a*(w^(b/(b - 1))/r^(b/(b - 1)) + 1))/OverBar[y])^ (-b^(-1))}} Of course in general you can't expect to get in this way the complete solution nor indeed that what you do get is a solution at all. This has to be verified by hand. Andrzej Kozlowski On 7 Dec 2004, at 18:09, yehuda ben-shimol wrote: > > The problem at hand is easily solved by hand in about 60 seconds. > Yehuda > > -----Original Message----- > From: Steve Luttrell To: mathgroup at smc.vnet.net > [mailto:steve_usenet at _removemefirst_luttrell.org.uk] > To: mathgroup at smc.vnet.net > Subject: [mg52683] [mg52659] [mg52636] Re: Solve given that a variable is > between 0 and 1 > > To solve algebraically you need to give a numerical value to b, and > then > only certain values lead to simple closed-form solution. Otherwise, > you have > > to solve numerically. > > Algebraic example: > > b = 1/2; > Solve[w - k^(1 - b)*r*((-((a*k^b - OverBar[y])/a))^ > (1/b))^(-1 + b) == 0, k] > > gives > > {{k -> (w^2*OverBar[y]^2)/(a^2*(-r + w)^2)}, > {k -> (w^2*OverBar[y]^2)/(a^2*(r + w)^2)}} > > Numerical example: > > b = 0.4; > w = 1; > a = 1; > r = 1; > OverBar[y] = 1; > NSolve[w - k^(1 - b)*r*((-((a*k^b - OverBar[y])/a))^ > (1/b))^(-1 + b) == 0, k] > > gives > > {{k -> 0.17677669529663688110021109052621}} > > Steve Luttrell > > "Jason" <jsr123 at gmail.com> wrote in message > news:cos13d$dl2$1 at smc.vnet.net... >> Hi all, >> >> I need some help with solving the following: >> >> \!\(Solve[ >> w - k\^\(1 - b\)\ r\ \((\((\(-\(\(a\ k\^b - >> y\&_\)\/a\)\))\)\^\(1\/b\))\)\ >> \^\(\(-1\) + b\) \[Equal] 0, k]\) >> >> given that a>0 and 0<b<1. >> >> How do I do this? >> >> Thanks MUCH!!---jason >> > > >
- References:
- Re: Re: Solve given that a variable is between 0 and 1
- From: "yehuda ben-shimol" <benshimo@bgu.ac.il>
- Re: Re: Solve given that a variable is between 0 and 1