If a + b = 5 and a - b = 3, then the value of (a² + b²) is?

Solution (By Examveda Team)

$$\eqalign{ & a + b = 5{\text{ }} \cr & \Leftrightarrow {a^2} + {b^2} + 2ab = 25\,.....(i) \cr & a - b = 3 \cr & \Leftrightarrow {a^2} + {b^2} - 2ab = 9\,.....(ii) \cr & {\text{From equation (i) and (ii)}} \cr & \Leftrightarrow {\text{2}}\left( {{a^2} + {b^2}} \right) = 34 \cr & \Leftrightarrow {a^2} + {b^2} = 17 \cr} $$