Nested Relations

Algebra Level 3

\( \huge x=\frac{1}{y+\frac{1}{y+\frac{1}{y+\frac{1}{y+...}}}} \)

\( \large y=\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+...}}}}} \)

Given that \(x\) and \(y\) are numbers that satisfy the relations given above, determine the exact value of

\( \left(\left(\frac{1}{y}\right)^{2\left(2014\right)}+x^{2014}\right)\left(\left(\frac{1}{x}\right)^{2014}+\left(y\right)^{2\left(2014\right)}\right) \)

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