If a² + b² = 2 and c² + d² = 1, then the value of (ad - bc)² + (ac - bd)² is?

Solution (By Examveda Team)

$$\eqalign{ & {a^2} + {b^2} = 2{\text{ }} \cr & {c^2} + {d^2} = 1 \cr & {\text{Put values of }}a,{\text{ }}b,{\text{ }}c,{\text{ }}d \cr & {\text{Take ,}}a = b = 1 \cr & c = 1 \cr & d = 0 \cr & \Rightarrow {\left( {ad - bc} \right)^2}{\text{ + }}{\left( {ac - bd} \right)^2} \cr & \Rightarrow {\left( {0 - 1} \right)^2} + {\left( {1 + 0} \right)^2} \cr & \Rightarrow {\left( { - 1} \right)^2} + {\left( 1 \right)^2} \cr & \Rightarrow 2 \cr} $$