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Re: Solving simultaneous equations with inequalities


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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