If a + b = 10 and ab = 21, then the value of (a - b)² is?

Solution(By Examveda Team)

$$\eqalign{ & a + b = 10{\text{ and }}ab = 21 \cr & \left( {a + b} \right) = 10 \cr & \Rightarrow {a^2} + {b^2} + 2ab = 100 \cr & \Rightarrow {a^2} + {b^2} = 100 - 2ab \cr & \Rightarrow {a^2} + {b^2} = 100 - 2 \times 21 \cr & \Rightarrow {a^2} + {b^2} = 100 - 42 \cr & {a^2} + {b^2} = 58\,.........(i) \cr & {\left( {a - b} \right)^2} = {a^2} + {b^2} - 2ab \cr & {\left( {a - b} \right)^2} = 58 - 2 \times 21 \cr & \left[ {{\text{from equation (i)}}} \right] \cr & = {\text{58}} - {\text{42}} \cr & {\left( {a - b} \right)^2} = 16 \cr} $$