Question

se (x-y)^2 - (x+y)^2 = -20, entao x.y é igual a:
(A) -1
(B) 0
(C) 10
(D) 5
(E) 1/5

Answer 1

(x-y)² - (x+y)² = -20
(x² - 2xy + y²) - (x² + 2xy + y²) = -20
-4xy = -20
xy = 5

Answer 2

$(x-y)^2-(x+y)^2=-20\\ \\ x^2-2xy+y^2-(x^2+2xy+y^2)=-20\\ \\ x^2-2xy+y^2-x^2-2xy-y^2=-20\\ \\ -4xy=-20\\ \\ \boxed{xy=5}$