Bunuel wrote:

If x and y are non-zero integers then the value of \([\frac{2}{\frac{1}{x^{(-2)}}+\frac{1}{y^{(-2)}}}]^{(-2)}\) can be expressed as

A. \(\frac{4}{x^4+2x^2y^2+y^4}\)

B. \(\frac{1}{x+y}\)

C. \(\frac{x^4+y^4}{4}\)

D. \(\frac{x^2+2xy+y^2}{4}\)

E. \(\frac{x^4+2x^2y^2+y^4}{4}\)

\([\frac{2}{\frac{1}{x^{(-2)}}+\frac{1}{y^{(-2)}}}]^{(-2)}\)

\([\frac{2}{\frac{x^{2}}{1}+\frac{y^{2}}{1}}]^{(-2)}\)

\([\frac{2}{x^{2}+y^{2}}]^{(-2)}\)

\([\frac{x^{2}+y^{2}}{2}]^{2}\)

\(\frac{(x^{2}+y^{2})^{2}}{4}\)

\(\frac{x^4+2x^2y^2+y^4}{4}\)

Answer (E)...