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