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Re: Solving simultaneous equations with inequalities
*To*: mathgroup at smc.vnet.net
*Subject*: [mg31153] Re: [mg31140] Solving simultaneous equations with inequalities
*From*: BobHanlon at aol.com
*Date*: Sun, 14 Oct 2001 04:11:46 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
In a message dated 2001/10/13 2:48:55 AM, milstead at cs.bris.ac.uk writes:
>I am solving some simultaneous equations and getting four results because
>the solution contains two square roots - produced because some of the
>equations to solve are of the form x^2 = y^2 + z^2. Is there any way of
>including the hint x>0 or 'I only want positive roots of x to be used'
>in
>Solve[]?
>
For a positive value of x, both y and z must be real and
at least one of them must be non-zero.
Select[
Solve[x^2==y^2+z^2, x],
Simplify[Positive[x/.#], Element[{y,z}, Reals]&&(y!=0||z!=0)]&]
{{x -> Sqrt[y^2 + z^2]}}
For a nonnegative value of x
Select[
Solve[x^2==y^2+z^2, x],
Simplify[NonNegative[x/.#], Element[{y,z}, Reals]]&]
{{x -> Sqrt[y^2 + z^2]}}
Bob Hanlon
Chantilly, VA USA
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