Solving inequalities.
- To: mathgroup at smc.vnet.net
- Subject: [mg45168] Solving inequalities.
- From: gtsavdar at auth.gr (George)
- Date: Fri, 19 Dec 2003 06:57:34 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
I want to solve this equation: f'(p)=0.
With the restrictions 0<p<1 and 2<k<n and
f(p) = (p^k) * (1-p)^(n-k).
How this can be done inside Mathematica 5.0 or 4.2?
The following procedure doesn't work.
I define the f[p_] and then i enter:
Needs["Algebra`InequalitySolve`"]
InequalitySolve[f'[p] == 0 && 1 > p > 0 && k > 2 && n > k, p]
but no solution is found.
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The above problem is "the same" with the equation:
x^(a+1) * (1-x)^(b-1) = (x^a) * (1-x)^b with the restrictions
0<x<1 and 1<b<a.
So this equation is the same with the: x = 1-x <=> x=0.5
But how can i solve this in Mathematica 5.0 or 4.2?
The:
Needs["Algebra`InequalitySolve`"]
InequalitySolve[x^(a+1) * (1-x)^(b-1) == (x^a) * (1-x)^b && 1 > x > 0
&& a > b > 1, x]
doesn't work.
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And generally because in Mathematica 5.0, Reduce can solve
inequalities,
how can i solve the (a^b)*(b^a)>0 with a>b>0. (Which is true of
course)
The: Reduce[(a^b)*(b^a)>0 && a>b>0,{a,b}] doesn't find it.
- Follow-Ups:
- Re: Solving inequalities.
- From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
- Re: Solving inequalities.