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The result of Df(x1,x2) is a vector with symbolic entries, and testing equality with the tuple (0, 0) returns False, hence the error.

If you want to use solve then you need either a list of equations or a list of left-hand sides of equations which will be set equal to zero. For equalities of vectors, a trick is to subtract right-hand sides from left-hand sides to obtain a single vector, and convert that to a list of entries:

sage: solve(list(Df(x1,x2) - vector([0,0])), (x1,x2))
[[x1 == 0, x2 == 0]]

In this specific case where right-hand sides of equations are already zero, the step of subtracting the right-hand side can of course be omitted.