First, we convert the magnitudes of the two stars to
a ratio of intensities.  Call the intensity of the
brighter star Mizar to be 1 unit.  Then

         I(Alcor)        -0.4 ( m(Alcor) - m(Mizar) )
        ---------   =  10
         I(Mizar)

                         -0.4 ( 4.00 - 2.05 )
                    =  10


                    =  0.166


  So, the combined intensity of the light from 
the two stars is 1.0 + 0.166 = 1.166 times the 
intensity of Mizar alone.  Now, convert that ratio
of intensity to a difference in magnitude.

     
       mag (combined) - mag(Alcor)  =   -2.5 * log10 (1.166)

                                    =   -0.167
  
  Thus

       mag (combined)   =  mag(Alcor) - 0.167
 
                        =  1.89