Re: Need help for a simple equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg12832] Re: [mg12813] Need help for a simple equation*From*: Daniel Lichtblau <danl>*Date*: Fri, 12 Jun 1998 18:15:10 -0400*References*: <199806120805.EAA24568@smc.vnet.net.>*Sender*: owner-wri-mathgroup at wolfram.com

Tae-Wan Kim wrote: > > Hello, > > I need your help to solve a simple equation. > > My problem is as follows: > f(x, y) = a x^2 + b xy + c y^2 + d x + e y + f = 0 (1) > > partial derivative of f(x,y) with respect to x: dfx(x, y) = 2 a x + b y > + d = 0 (2) > > I'd like to solve (1) and (2) using Mathematica. > > I get two set of roots: > (x_0, y_0) and (x_1, y_1) > > I programmed as sollows: > SetAttributes[a, Constant] > SetAttributes[b, Constant] > SetAttributes[c, Constant] > SetAttributes[d, Constant] > SetAttributes[e, Constant] > SetAttributes[f, Constant] > f[x_, y_] := a x^2 + b xy + c y^2 + d x + e y + f > > dfx = D[f[x,y], x] > -> this didn't work > > I don't know what to do here. > > Could you please tell me Mathematics program to solve this problem? > > Thank you. > > Best regards, > > Tae-wan Kim > SDRC The devil is in the details. First problem: "xy" is not the same as "x*y". Second (minor) problem: it is dangerous practice to use the same symbol in two different ways. This applies to "f" in your definition. For the particular stated purpose there is really no need to define a "function" f so I'll change this a bit as well. In[19]:= fxy = a*x^2 + b*x*y + c*y^2 + d*x + e*y + g; In[20]:= dfx = D[fxy,x] Out[20]= d + 2 a x + b y In[21]:= Solve[{fxy,dfx}==0, {x,y}] // InputForm Out[21]//InputForm= {{x -> (-d - (b^2*d)/(-b^2 + 4*a*c) + (2*a*b*e)/(-b^2 + 4*a*c) - (2*Sqrt[a]*b*Sqrt[c*d^2 - b*d*e + a*e^2 + b^2*g - 4*a*c*g])/ (-b^2 + 4*a*c))/(2*a), y -> (b*d - 2*a*e + 2*Sqrt[a]*Sqrt[c*d^2 - b*d*e + a*e^2 + b^2*g - 4*a*c*g])/(-b^2 + 4*a*c)}, {x -> (-d - (b^2*d)/(-b^2 + 4*a*c) + (2*a*b*e)/(-b^2 + 4*a*c) + (2*Sqrt[a]*b*Sqrt[c*d^2 - b*d*e + a*e^2 + b^2*g - 4*a*c*g])/ (-b^2 + 4*a*c))/(2*a), y -> (b*d - 2*a*e - 2*Sqrt[a]*Sqrt[c*d^2 - b*d*e + a*e^2 + b^2*g - 4*a*c*g])/(-b^2 + 4*a*c)}} Daniel Lichtblau Wolfram Research

**References**:**Need help for a simple equation***From:*Tae-Wan Kim <tae-wan.kim@sdrc.com>