If $$\sqrt {\left( {1 - {p^2}} \right)\left( {1 - {q^2}} \right)} = \frac{{\sqrt 3 }}{2},$$     then what is the value of $$\sqrt {2{p^2} + 2{q^2} + 2pq} + \sqrt {2{p^2} + 2{q^2} - 2pq} \,?$$

Solution (By Examveda Team)

$$\eqalign{ & \sqrt {\left( {1 - {p^2}} \right)\left( {1 - {q^2}} \right)} = \frac{{\sqrt 3 }}{2}\,........\,\left( {\text{i}} \right) \cr & {\text{Put value of }}p{\text{ and }}q \cr & p = 0,\,q = \frac{1}{2} \cr & {\text{Equation }}\left( {\text{i}} \right){\text{ is satisfying}} \cr & {\text{Then, }} \cr & \sqrt {2{p^2} + 2{q^2} + 2pq} + \sqrt {2{p^2} + 2{q^2} - 2pq} \cr & = \sqrt {0 + \frac{2}{4} + 0} + \sqrt {0 + \frac{2}{4} - 0} \cr & = \frac{1}{{\sqrt 2 }} + \frac{1}{{\sqrt 2 }} \cr & = \frac{2}{{\sqrt 2 }} \cr & = \sqrt 2 \cr} $$