Two periodic waves of intensities I_1 and I_2 pass through a region...

Resultant intensity of two periodic waves is given by $I=I_1+I_2+2 \sqrt{I_1 I_2} \cos \delta$ where $\delta$ is the phase difference between the waves. For maximum intensity, $\delta=2 n \pi ; n=0,1,2 \ldots$ etc. Therefore, for zero order maxima, $\cos \delta=1 I_{\text{max }}=I_1+I_2+2 \sqrt{I_1 I_2}=\left(\sqrt{I_1}+\sqrt{I_2}\right)^2 For minimum intensity,$\delta=(2 n-1) \pi$;$n=1,2 \ldots $\text{ etc }$ Therefore, for Ist order minima, $\cos \delta=-1$ $$\begin{aligned} I_{\min } & =I_1+I_2-2 \sqrt{I_1 I_2} \\ & =\left(\sqrt{I_1}-\sqrt{I_2}\right)^2 \end{aligned}$$$Therefore,$$\begin{aligned} I_{\max }+I_{\min } & =\left(\sqrt{I_1}+\sqrt{I_2}\right)^2+\left(\sqrt{I_1}-\sqrt{I_2}\right)^2 \\ & =2 \left(I_1+I_2\right) \end{aligned}$$