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

Answer: Option A

$$\begin{array}{rl}& a+b=5\\ & \iff a^2+b^2+2ab=25.....(i)\\ & a-b=3\\ & \iff a^2+b^2-2ab=9.....(ii)\\ & \text{From equation (i) and (ii)}\\ & \iff \text{2}\left(a^2+b^2\right)=34\\ & \iff a^2+b^2=17\end{array}$$