If x - y = 2, xy = 24, then the value of (x² + y²) is?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Given,}} \cr & x - y = 2{\text{ and }}xy = 24 \cr & {\text{By squaring}} \cr & \Rightarrow {x^2} + {y^2} - 2xy = 4 \cr & \Rightarrow {x^2} + {y^2} - 2 \times 24 = 4 \cr & \Rightarrow {x^2} + {y^2} = 4 + 48 \cr & \Rightarrow {x^2} + {y^2} = 52 \cr} $$