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SMO 2017 Senior Round 1 Question 5

SMO · SMO 2017 Senior Round 1

Question 5

Simplify $$\frac{(\sqrt5)^3-(\sqrt2)^3}{\sqrt5-\sqrt2}-\frac{(\sqrt5)^3+(\sqrt2)^3}{\sqrt5+\sqrt2}.$$
  1. $\sqrt{10}$
  2. $2\sqrt{10}$
  3. $3\sqrt{10}$
  4. $\sqrt5-\sqrt2$
  5. $\sqrt5+\sqrt2$