Re: Is this a problem in mathematica?

*To*: mathgroup at smc.vnet.net*Subject*: [mg74668] Re: [mg74615] Is this a problem in mathematica?*From*: Carl Woll <carlw at wolfram.com>*Date*: Fri, 30 Mar 2007 03:01:32 -0500 (EST)*References*: <200703280644.BAA20508@smc.vnet.net>

traz wrote: >Let's say I wanna solve this problem: > >Determine point(s) on y = x^2 +1 that are >closest to (0,2). > >So in mathematica: > >minDist = (x - 0)^2 + (y - 2)^2; >Minimize[minDist, y == 1 + x^2, {x, y}] > >Output will give you: x -> -1/Sqrt[2], y -> 3/2 > >but x also has another answer: +1/Sqrt[2]. Is this a problem in mathematica or can my code be changed to output the other value of x for the minimum distance? > > Another possibility besides those menioned by others is to use Solve once you know the minimum: minDist=(x-0)^2+(y-2)^2; Minimize[minDist,y==1+x^2,{x,y}] {3/4,{x->-1/Sqrt[2],y->3/2}} Solve[{minDist==3/4,y==1+x^2},{x,y}] {{y->3/2,x->-1/Sqrt[2]},{y->3/2,x->-1/Sqrt[2]},{y->3/2,x->1/Sqrt[2]},{y->3/2,x->1/Sqrt[2]}} Carl Woll Wolfram Research

**References**:**Is this a problem in mathematica?***From:*traz <t_raz@yahoo.com>