When two periodic waves of intensities $I_1$ and $I_2$ superimpose, the resultant intensity $I$ at a point is given by: $I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$ where $\phi$ is the phase difference between the waves. For maximum intensity, $\cos \phi = 1$: $I_{max} = I_1 + I_2 + 2\sqrt{I_1 I_2} = (\sqrt{I_1} + \sqrt{I_2})^2$ For minimum intensity, $\cos \phi = -1$: $I_{min} = I_1 + I_2 - 2\sqrt{I_1 I_2} = (\sqrt{I_1} - \sqrt{I_2})^2$ The sum of the maximum and minimum intensities is: $I_{max} + I_{min} = (I_1 + I_2 + 2\sqrt{I_1 I_2}) + (I_1 + I_2 - 2\sqrt{I_1 I_2}) = 2(I_1 + I_2)$