Re: Solve given that a variable is between 0 and 1

*To*: mathgroup at smc.vnet.net*Subject*: [mg52636] Re: Solve given that a variable is between 0 and 1*From*: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>*Date*: Sun, 5 Dec 2004 02:08:17 -0500 (EST)*References*: <cos13d$dl2$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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 >