Explanation

(d) Resultant intensity of two periodic wave 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, $\delta$=2nπ; n=0,1,2,…. Etc.
Therefore, for zero order maxima, cos $\delta$=1
$I_{\max\ } = I_{1} + I_{2} + 2\sqrt{I_{1}I_{2}}$
$= \left( \sqrt{I_{1}} + \sqrt{I_{2}} \right)^{2}$
For minimum intensity, $\delta$=(2n-1)π;
N=1,2,…etc
Therefore, for Ist order minima, cos $\delta$=-1
$I_{\max\ } = I_{1} + I_{2} - 2\sqrt{I_{1}I_{2}}$
$= \left( \sqrt{I_{1}} - \sqrt{I_{2}} \right)^{2}$
$Therefore,I_{\max\ } + I_{\min\ } = \left( \sqrt{I_{1}} + \sqrt{I_{2}} \right)^{2} + \left( \sqrt{I_{1}} - \sqrt{I_{2}} \right)^{2}$
$= 2\left( I_{1} + I_{2} \right)$