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Question about Solve (on mma2.2)


Hello,

Please tell me how to get roots(intersection?) of simultaneous 
nonlinear equations  when variables are REAL. 

Example1: [ x,y,z are real variables.]
---
f1 =      x^2 + y^2 + z^2 -1;
f2 =  (x-2)^2 + y^2 + z^2 -1;
Solve[ f1==0 && f2==0, {x,y,z}]

Out[3]= {{y -> -I z, x -> 1}, {y -> I z, x -> 1}}
---

    {x->1,y->0,z->0} is a result that I want.

Example2: [ x,y,z are real variables.]
---
f1 =      x^2 + y^2 + z^2 -1;
f2 =  (x-5)^2 + y^2 + z^2 -1;
Solve[ f1==0 && f2==0, {x,y,z}]

                           2                             2
Out[3]= {{y -> -Sqrt[-3 - z ], x -> 2}, {y -> Sqrt[-3 - z ], x -> 2}}

---
In this case , {f1==0} does not intersect {f2==0} and
Sqrt[-3-z^2] is not real when z is real.
My ideal result is a null list.

Is it necessary to use a Package for nonlinear programming ?

Thanks in advance.

HARASHIMA Seigo ( haras at vermeer.c.u-tokyo.ac.jp )





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