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1991 AMC 12 Question 27

AMC12 · 1991 AMC 12

Question 27

If $$
\begin{aligned} x+\sqrt{x^2-1} &+\frac1{x-\sqrt{x^2-1}}\\ &=20, \end{aligned}
$$ then $$
\begin{aligned} x^2+\sqrt{x^4-1} &+\frac1{x^2+\sqrt{x^4-1}}\\ &= \end{aligned}
$$
  1. $5.05$
  2. $20$
  3. $51.005$
  4. $61.25$
  5. $400$