If a + b = 12, ab = 22, then (a2 + b2) is equal to?

Answer: Option D

$$\begin{array}{rl}& a+b=12.....\text{(i)}\\ & ab=22.....\text{(ii)}\end{array}$$
Squaring both sides of equation (i)
$$\begin{array}{rl}& \Rightarrow a^2+b^2+2ab=144\\ & \Rightarrow a^2+b^2+2\times 22=144\\ & \Rightarrow a^2+b^2=144-44\\ & \Rightarrow a^2+b^2=100\end{array}$$