  The aim of this paper is to get a complete list of positive definite
symmetric matrices with integer entries $\a&b\b&d\$ such that all complex
solutions to the system of equations $1-x_1=x_1^ax_2^b\ 1-x_2=x_1^bx_2^d$ are
real. This result is related to Nahm's conjecture in rank 2 case.
