       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
>

```

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