# Question:3-D system: how many solutions?

## Question:3-D system: how many solutions?

Hi there,

So my problem is to find the solution(s) of a 3-D system. I can get Maple to spit out a solution (at times), but I am looking for reassurance that this is indeed the solution (if unique, and if not what the other solutions may be). Increasing Digits makes Maple "lose" the solution and return a blank-- normal behavior? Looking at the 3-D plot of the system offers something to puzzle over.

I set up the system in  (x,c,q):

xd := x^.5-.1*x-c;
cd := (.5/x^.5-.1-q)*c;
qd := -(q-.2e-1)*(q-.3e-1)+(q-.25e-1)*(.5/x^.5-.1-q)*c/(x^.5-.1*x-c);

I look for a solution with fsolve:

Digits:=10: interface(displayprecision=10):
ss:= fsolve({xd,cd/c,qd}, {x,c,q}, avoid={x=0, c=0, q=0});
xs:=subs(ss,x): cs:=subs(ss,c): qs:=subs(ss,q):

Maple gives:

ss := {c = 2.399289639, q = .2511089584e-1, x = 15.97164840}

If I raise digits to 15, Maple can't solve it anymore. Perhaps this is normal behavior.

I'd like some reassurance that this solution is indeed a solution. Simply feeding the fsolve output back into the system will not work because of a division by zero:

eval(xd,{x=xs,c=cs,q=qs}); eval(cd,{x=xs,c=cs,q=qs}); eval(qd,{x=xs,c=cs,q=qs});

yields:

0.
-.9597158556e-10
Float(-infinity)

I decided to look at the 3-D plot. The plot of the system suggests that there may be several solutions.

The plot: