Correct Answer - Option 2 : 11
Given:
x4 + y4 + x2y2 = 576 and xy = 7
Formula used:
(x + y)2 = x2 + y2 + 2xy
Calculations:
x4 + y4 + x2y2 = 576
Adding x2y2 in both side of the equation.
⇒ (x2 + y2)2 – x2y2 = 576
⇒ (x2 + y2)2 – (7)2 = 576
⇒ (x2 + y2)2 – 49 = 576
⇒ (x2 + y2)2 = 576 + 49 = 625
⇒ (x2 + y2) = 25
Thus x2 + y2 - 2xy = 25 - 2 × 7 = 11
⇒ (x - y)2 = 11
∴ The value of (x - y)2 is 11.