If x4 + x2y2 + y4 = 21, x2 + xy + y2 = 3, then find 4xy.

Formula → x⁴ + y⁴ + x²y² = (x² + y² + xy) × (x² + y² - xy)

⇒ 21 = 3 × (x² + y² - xy)

⇒ x² + y² - xy = \(\frac{21}{3}\) = 7   .........(i)

⇒ x² + y² +  xy = 3    (given) .............(ii)

Now, (ii) - (i)

⇒ 2xy = - 4

⇒ 4xy = -8