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AHSME 1991 Problem 27

    If x+x2−1+1x−x2−1=20,x+\sqrt{x^2-1}+\frac{1}{x-\sqrt{x^2-1}}=20, then x2+x4−1+1x2+x4−1=x^2+\sqrt{x^4-1}+\frac{1}{x^2+\sqrt{x^4-1}}= (A) 5.05(B) 20(C) 51.005(D) 61.25(E) 400\textbf{(A) } 5.05 \textbf{(B) } 20 \textbf{(C) } 51.005 \textbf{(D) } 61.25 \textbf{(E) } 400

    Dataset text NuminaMath-1.5. Quoted with source.

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    51.005

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