Mean value theorem

  • Thread starter steffka
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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

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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

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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

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sorry, meant it to be -1 not 1.
 
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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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