If x² + y² - 4x - 4y + 8 = 0, then the value of x - y is?

Solution (By Examveda Team)

$$\eqalign{ & {x^2} + {y^2} - 4x - 4y + 8 = 0 \cr & \Rightarrow {x^2} + 4 - 4x + {y^2} + 4 - 4y = 0 \cr & \Rightarrow {\left( {x - 2} \right)^2} + {\left( {y - 2} \right)^2} = 0 \cr & {\left( {x - 2} \right)^2} = 0 \Leftrightarrow x = 2 \cr & {\left( {y - 2} \right)^2} = 0 \Leftrightarrow y = 2 \cr & \therefore x - y \cr & \Rightarrow 2 - 2 \cr & \Rightarrow 0 \cr} $$