Respuesta :

Lazerpent

Take your original equation [tex] \frac{x}{y} +\frac{y}{x} =-1 [/tex]

and multiply both sides by [tex] xy [/tex] to remove the fractions. You are left with

[tex] x^2+y^2=-xy [/tex]

So, [tex] x^2+y^2=-xy [/tex]

Update: There is no numerical answer that can be found without being given a value for either x or y

konrad509

[tex] \dfrac{x}{y}+\dfrac{y}{x}=-1|\cdot xy\\\\
x^2+y^2=-xy\\\\
x^2+xy+y^2=0\\\\
\boxed{x^3-y^3=(x+y)(x^2+xy+y^2)}\\
\Downarrow\\
x^3-y^3=(x+y)\cdot 0\\\\
\boxed{\boxed{x^3-y^3=0}}
[/tex]