If x4 + x2y2 + y4 = 273 x2 - xy + y2 = 13, then find xy.

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

⇒ 273 = 13 × (x² + y² + xy)

⇒ x² + y² + xy = \(\frac{273}{13}\)

⇒ x² + y² + xy = 21                 ............(i)

⇒ x² + y² -  xy = 13    (given) .............(ii)

(i) - (ii),

⇒ 2xy = 8

⇒ xy = 4