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SMO 2005 Senior Round 1 Question 9

SMO · SMO 2005 Senior Round 1

Question 9

Simplify
$$\sqrt{2\left(1+\sqrt{1+\left(\frac{x^4-1}{2x^2}\right)^2}\right)},$$
where $x$ is any positive real number.
  1. $\frac{x^2+1}{\sqrt2x}$
  2. $\frac{x^2+1}{x}$
  3. $\sqrt{\frac{x^2+1}{2x^2}}$
  4. $x^2+1$
  5. $\frac{x^2-1}{\sqrt2x}$