1991 AHSME Problems/Problem 27

Problem

If $x+\sqrt{x^2-1}+\frac{1}{x-\sqrt{x^2-1}}=20$ then $x^2+\sqrt{x^4-1}+\frac{1}{x^2+\sqrt{x^4-1}}=$

(A) $5.05$ (B) $20$ (C) $51.005$ (D) $61.25$ (E) $400$

Solution by e_power_pi_times_i

Notice that the first equation equates to $\dfrac{x^2 - (x^2 - 1) + 1}{x - \sqrt{x^2 - 1}} = 20$ . Therefore

1991 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 26	Followed by Problem 28
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