  The paper considers the problem of finding the range of functional I = J f (z
0), f (z 0), F ($\zeta$ 0), F ($\zeta$ 0) , defined on the class M of pairs
functions (f (z), F ($\zeta$)) that are univalent in the system of the disk and
the interior of the disk, using the method of internal variations. We establish
that the range of this functional is bounded by the curve whose equation is
written in terms of elliptic integrals, depending on the parameters of the
functional I.
