Given that,

x + y = 4 and xy=2

We take the equation: x + y = 4 and on squaring both sides, we get

(x + y)² = 4²

x² + y² + 2xy = 16

x² + y² + 2 (2) = 16  (Because xy=2 is given)

x² + y² + 4  = 16

x² + y² = 16 – 4

x² + y² =12

Therefore, the value of x² + y² is 12