If a(x + y) = b(x - y) = 2ab, then the value of 2(x² + y²) is?

Solution (By Examveda Team)

$$\eqalign{ & a\left( {x + y} \right) = b\left( {x - y} \right) = 2ab \cr & x + y = 2b \cr & {\text{On squraing both side}} \cr & \Rightarrow {x^2} + {y^2} + 2xy = 4{b^2}\,.....(i) \cr & \Rightarrow b\left( {x - y} \right) = 2ab \cr & \Rightarrow x - y = 2a \cr & {\text{On squraing both side}} \cr & \Rightarrow {x^2} + {y^2} - 2xy = 4{a^2}\,.....(ii) \cr & {\text{Add equation (i) and (ii)}} \cr & \Rightarrow 2\left( {{x^2} + {y^2}} \right) = 4\left( {{a^2} + {b^2}} \right) \cr} $$