The interference pattern is obtained with two coherent light...

The ratio of the intensities is $\dfrac{{I}_{1}}{{I}_{2}} = \dfrac{4}{1}$

After taking square root of above equation on both sides, we get, $\dfrac{\sqrt{{I}_{1}}}{\sqrt{{I}_{2}}} = \dfrac{2}{1}$

Apply componendo and dividendo,
$⇒ \dfrac{\sqrt{{I}_{1}} + \sqrt{{I}_{2}}}{\sqrt{{I}_{1}} - \sqrt{{I}_{2}}} = \dfrac{2 + 1}{2 - 1} = \dfrac{3}{1}$
⇒ {\left(\dfrac{\sqrt{{I}_{1}} + \sqrt{{I}_{2}}}{\sqrt{{I}_{1}} - \sqrt{{I}_{2}}}\right)}^{2} = \dfrac{{I}_\max}{{I}_\min} = \dfrac{9}{1} ⇒ \dfrac{{I}_\max + {I}_\min}{{I}_\max - {I}_\min} = \dfrac{10}{8} = \dfrac{5}{4}

Therefore, the answer is $4$.