Question

(Mack-SP) Se ( x- y )² - ( x + y )² = - 20, então x . y é igual a:​

Answer 1

temos que

$(x-y)^2=x^2-2xy+y^2$

e

$(x+y)^2=x^2+2xy+y^2$

então

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