The resultant intensity is given by Inet=I1+I2+2I1I2cosϕ
Now, for Imax, phase angle is ϕ=0 and for Imin, phase angle is ϕ=π.
Thus, Imax=(I1+I2)2=(9I+4I)2=25I
And Imin=(I1−I2)2=(9I−4I)2=I
The difference of resultant intensities is Imax−Imin=25I−I=24I