  In the X(3872) decay, both of the J/\psi\pi\pi\ and J/\psi\pi\pi\pi\
branching fractions are observed experimentally, and their sizes are comparable
to each other. In order to clarify the mechanism to cause such a large isospin
violation, we investigate X(3872) employing a model of coupled-channel
two-meson scattering with a ccbar core. The two-meson states consist of
D0Dbar*0, D+Dbar*-, J/\psi\rho, and J/\psi\omega. The effects of the \rho\ and
\omega\ meson width are also taken into account.
  We calculate the transfer strength from the ccbar core to the final two-meson
states. It is found that very narrow J/\psi\rho\ and J/\psi\omega\ peaks appear
very close to the D0Dbar*0 threshold for a wide range of variation in the
parameter sets. The size of the J/\psi\rho\ peak is almost the same as that of
J/\psi\omega, which is consistent with the experiments. The large width of the
\rho\ meson makes the originally small isospin violation by about five times
larger.
