I have a system of $n$ quadratic equations with $n$ unknowns. It can be written as

$diag(x)Ax=1$

$x$ is an $n$-vector, $A$ is $n\times n$, real, symmetric and positive definite, the diagonal elements of $A$ are strictly positive, other elements of $A$ are arbitrary, $1$ is a vector of ones and $diag(x)$ is just s shorthand for taking a vector and putting it on the diagonal of a matrix, the rest of the entries are all zeros.

I am interested in the following question:

- How many strictly positive solutions exist (in general)?

Any help (examples etc). is greatly appreciated!