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x/ y + y/x = -1
(x^2+y^2)/xy= -1
x^2 + y^2= - xy -- (1)
x^3-y^3= ( x-y)(x^2+y^2+xy) -- (2)
Substitute equation (1) in equation (2)
x^3-y^3= (x-y)( -xy + xy)
x^3-y^3= (x-y)(0)
Therefore,
x^3-y^3= 0
Hope it helps!
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