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SMO 2011 Senior Round 1 Question 6

SMO · SMO 2011 Senior Round 1

Question 6

Determine the value of
$$\frac{2}{\frac1{\sqrt2+\sqrt[4]8+2}+\frac1{\sqrt2-\sqrt[4]8+2}}.$$
  1. $4-\sqrt2$
  2. $2-2\sqrt2$
  3. $4+\sqrt2$
  4. $2\sqrt2+4$
  5. $4\sqrt2-2$