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2 stage solution with FindRoot


I have a function f[X1,X2], where X1 and X2 are vectors of variables
x1[i] and x2[i], i=1,...,n. I need to solve the problem the following
way. First, I need to solve for  X1={X1|D[f[X1,X2],X1]==0}.  Then,
substituting X1 into f[.] I shall have f[X1[X2],X2]. I then need to
solve for X2={X2|D[f[X1[X2],X2],X2]==0}.  Since function f[.] is very
complicated Solve cannot handle it.  I have to use FindRoot.  I know I
have to use symbolic solution to a numerical function but I do not know
how exactly. I tried a couple of ways but have not succeeded. Please
advise.

PS.  I want to make it clear that I need 2 stage solution, not just 1
stage simultaneous solution to a set of 2n equations.


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