Question 446221
{{{x/y + y/x = -1}}}
<==> {{{(x^2 + y^2)/(xy) = -1}}}
<==> {{{x^2 + y^2 = -xy}}} ==> {{{x^2 + xy + y^2 = 0}}}

==>  {{{x^3 - y^3 = (x-y)(x^2 + xy  + y^2) = (x-y)*0 = 0}}}