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VTMO 2015 — Grade 9 — semifinal Question 12

VTMO · VTMO 2015 — Grade 9 — semifinal

Question 12

For distinct positive $a , b$, which expression is largest?
  1. $2 \frac{ab}{a + b}$
  2. $\sqrt{ab}$
  3. $\frac{a^{2} + b^{2}}{a + b}$
  4. $\frac{a + b}{2}$
  5. $\sqrt{\frac{a^{2} + b^{2}}{2}}$