1997 JBMO Problems/Problem 2: Difference between revisions
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== Problem == | == Problem == | ||
''(Cyprus)'' Let <math>\frac{x^2+y^2}{x^2-y^2} + \frac{x^2-y^2}{x^2+y^2} = k</math>. Compute the following expression in terms of <math>k</math>: | |||
<cmath> E(x,y) = \frac{x^8 + y^8}{x^8-y^8} - \frac{ x^8-y^8}{x^8+y^8}. </cmath> | |||
== Solution == | == Solution == | ||
. Compute the following expression in terms of 
:
![\[E(x,y) = \frac{x^8 + y^8}{x^8-y^8} - \frac{ x^8-y^8}{x^8+y^8}.\]](http://latex.artofproblemsolving.com/c/9/9/c99e935bc847cdcaee76b4a8af84db262067eca7.png)
