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x=1y+1y+1y+1y+... \huge x=\frac{1}{y+\frac{1}{y+\frac{1}{y+\frac{1}{y+...}}}} x=y+y+y+y+...1111
y=x+x+x+x+x+... \large y=\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+\sqrt{x+...}}}}} y=x+x+x+x+x+...
Given that xxx and yyy are numbers that satisfy the relations given above, determine the exact value of
((1y)2(2014)+x2014)((1x)2014+(y)2(2014)) \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) ((y1)2(2014)+x2014)((x1)2014+(y)2(2014))
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