Question

if x/y + y/x = -1 , ( x unequal y, y unequal 0) then the value of x^2 - y^2 is?

Answer 1

Take your original equation $\frac{x}{y} +\frac{y}{x} =-1$

and multiply both sides by $xy$ to remove the fractions. You are left with

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

So, $x^2+y^2=-xy$

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

Answer 2

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