Re: inequation

*To*: mathgroup at smc.vnet.net*Subject*: [mg13903] Re: inequation*From*: "Allan Hayes" <hay at haystack.demon.cc.uk>*Date*: Sun, 6 Sep 1998 02:55:40 -0400*References*: <6sil72$4at@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Client Préferé <@ping.be> wrote in message <6sil72$4at at smc.vnet.net>... >resoudre l inequatin > >(3-2x/x-1)² <ou=(6-5x/x+2)² > > >merci pour vos solution > > nicolas d aout > Nicolas, When x = 0 both sides are indeterminate. Otherwise we have (3 -2 -1)^3 <= (6 -5 +2)^2 <=> 0^2 <= 3^2 <=> 0 <= 9 <=> True Mathematica looks only at the general case ((3-2x/x-1)^2 <=(6-5x/x+2)^2) True However, you may have intended ((3-2x/(x-1))^2 <=(6-5x/(x+2))^2) And in this case we merely get ((3-2x/(x-1))^2 <=(6-5x/(x+2))^2) 2 x 2 5 x 2 (3 - ------) <= (6 - -----) -1 + x 2 + x However, we can load an Add-on Standard Package: <<Algebra`InequalitySolve` (these can be lloked up in the menu Help > Help > Add-ons > Standard Packages) and then we get InequalitySolve[((3-2x/(x-1))^2 <=(6-5x/(x+2))^2),x] Out[9]= 1 1 (- (-5 - Sqrt[61]) <= x) < -2 || (-2 < x) <= - || 2 2 1 x >= - (-5 + Sqrt[61]) 2 Of course, this still leaves out the special cases, x=1, x=-2. Best wishes ------------------------------------------------------------- Allan Hayes Mathematica Training and Consulting Leicester UK http://www.haystack.demon.co.uk hay at haystack.demon.co.uk voice: +44 (0)116 271 4198 fax: +44(0)116 271 8642