Numerical: algebraic identities MCQ - Practice Questions with Answers

Since x/y + y/x = 1, with x and y non-zero, multiplying by xy gives x^2 + y^2 = xy. Rearranging gives x^2 - xy + y^2 = 0. Now use the identity x^3 + y^3 = (x + y)(x^2 - xy + y^2). The second factor is zero, so the whole expression is 0. The values 1 and -1 are not obtained from this identity, and -xy is not equal to x^3 + y^3 under the given condition.