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