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
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