Question

Seja (x-y)²-(x+y)²=-80 . Determine x.y 

Answer 1

$(a + b)^{2}=a^{2}+2ab+b^{2} \\ (a - b)^{2}=a^{2}-2ab+b^{2}$
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$(x - y)^{2} - (x + y)^{2} = - 80$
$(x^{2} - 2xy + y^{2}) - (x^{2} + 2xy + y^{2})=-80$
$x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}=-80$
$(x^{2}-x^{2})+(-2xy-2xy)+(y^{2}-y^{2})=-80$
$-4xy=-80$
$4xy=80$
$xy=80/4$
$xy=20$