If x/y + y/x = - 1, find the value of x^3 - y^3

0

Step-by-step explanation:

Multiplying the first equation by xy, we have ...

x^2 + y^2 = - xy

Factoring the expression of interest, we have ...

x^3 - y^3 = (x - y) (x^2 + xy + y^2)

Substituting for xy using the first expression we found, this is ...

x^3 - y^3 = (x - y) (x^2 - (x^2 + y^2) + y^2) = (x - y) (0) = 0

The value of x^3 - y^3 is 0.