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

A. 188

B. 144

C. 34

D. 100

Answer: Option D

Solution(By Examveda Team)

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