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

0 \(\frac{5}{2}\) \(\frac{21}{4}\) \(\frac{6}{7}\)

\(\frac{21}{4}\)

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 = \(\frac{21}{4}\)