Question

sabendo que (x-y)² - (x+y)² = -20, qual o valor de x.y?

Answer 1

(x-y)² - (x+y)² = - 20
(x-y)(x-y) - (x+y)(x+y) = - 20
(x² - 2xy + y²) - (x² + 2xy + y²) = - 20
x² - 2xy + y² - x² - 2xy - y² = - 20
- 4xy = - 20  simplifique(-1)
4xy = 20
$xy = \frac{20}{4}$
$\boxed{xy = 5}$