If x = 1 - y x2 = 2 - y2 , then find the value of (xy)2 + 5.

Formula → (a + b)² = a² + b² + 2ab

⇒ x = 1 - y

x + y = 1

Squaring both sides,

(1)² = 2 + 2xy  (since x + y = 1 and  x² + y² = 2)

xy = -\(\frac{1}{2}\)

(xy)² + 5 =  \(\frac{1}{4}\) + 5 = \(\frac{21}{4}\)