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Omni-MATH / Let (x²+y²)/(x²−y²)+(x²−y²)/(x²+y²)=k. Compute the following expression in terms of k: E(x,y)=(x⁸+y⁸)/(x⁸−y⁸)−(x⁸−y⁸)/(x⁸+y⁸). [i]Ciprus[/i]

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let x2+y2x2−y2+x2−y2x2+y2=k\frac{x^2+y^2}{x^2-y^2} + \frac{x^2-y^2}{x^2+y^2} = k. Compute the following expression in terms of kk: E(x,y)=x8+y8x8−y8−x8−y8x8+y8. E(x,y) = \frac{x^8 + y^8}{x^8-y^8} - \frac{ x^8-y^8}{x^8+y^8}. [i]Ciprus[/i]
Plain-text mathematical notation (without MathML)
Let (x²+y²)/(x²−y²)+(x²−y²)/(x²+y²)=k. Compute the following expression in terms of k: 
E(x,y)=(x⁸+y⁸)/(x⁸−y⁸)−(x⁸−y⁸)/(x⁸+y⁸).
[i]Ciprus[/i]
Original LaTeX notation
Let $\frac{x^2+y^2}{x^2-y^2} + \frac{x^2-y^2}{x^2+y^2} = k$. Compute the following expression in terms of $k$: 
\[ E(x,y) = \frac{x^8 + y^8}{x^8-y^8} - \frac{ x^8-y^8}{x^8+y^8}.  \]
[i]Ciprus[/i]

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Source and history

task_id
b6dd9b65-d03c-5d0e-afa5-154f6711001c
task_key
test--b6dd9b65-d03c-5d0e-afa5-154f6711001c
task_revision_id
1
config / split
/ test

Official source

initial import