If x4 + x2y2 + y4 = 21 and x2 + xy + y2 = 3, then what is the value of (-xy)?

If x4 + x2y2 + y4 = 21 and x2 + xy + y2 = 3, then what is the value of (-xy)? Correct Answer 2

Given:

x4 + x2y2 + y4 = 21 and x2 + xy + y2 = 3

Formula used:

x4 + x2y2 + y⁴ = (x² – xy + y²) (x2 + xy + y²)

Calculation:

x4 + x2y2 + y4 = 21 

And, x2 + xy + y2 = 3 ......(1)

Now,

x4 + x2y2 + y4 = (x2 – xy + y2) (x2 + xy + y2)

⇒ 21 = (x2 – xy + y2) × 3

⇒ (x2 – xy + y2) = 7 ......(2)

Subtracting equation (2) from (1) we get,

(x2 – xy + y² = 7) – (x2 + xy + y2 = 3)

⇒ 2xy = (-4)

⇒ xy = (-4/2)

⇒ xy = -2

Now,

The value of -xy = 2

∴ The required value is 2