# Mean value theorem

Can someone help me... i need to show, that a system of 2 nonlinear equations
has a root. I think it is possible to use something like "mean value theorem". But i can not find any mean value theorem for R^n -> R^n.

matt grime
Homework Helper
the mean value theorem is not true in multiple dimensions, and unless you can be more specific your problem as stated is false, there is no real solution to

x^2+y^2=1

irrespective of the second equation over R, so are you talking about C?

VietDao29
Homework Helper
matt grime said:
the mean value theorem is not true in multiple dimensions, and unless you can be more specific your problem as stated is false, there is no real solution to

x^2+y^2=1
Hmmm, ... Yes, it does... x = 0, y = 1 is one example.
The one does not have real root is x^2 + y^2 = -1.
Viet Dao,

matt grime
Homework Helper
sorry, meant it to be -1 not 1.

correction resp. specification

I have two equations (nonlinear) with two variles. With some aproximative methods I get some potential roots (but not exact), so i know (or hope) there are some.
I need to show, that there exists at least one root.
I thought that somethinq like mena value theorem could help.

In attachment are equations and also the potential roots.
(the root x=0 and y=0 is trivial, but i need some other)

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