VTMO 2026 - Grade 9 - Semifinal - SET 2 - Self-study Question 4

Question 4

Let a and b be distinct positive numbers. Which of the following is largest?

1. $\frac{2ab}{a+b}$
2. $\sqrt{ab}$
3. $\frac{a^2+b^2}{a+b}$
4. $\frac{a+b}{2}$
5. $\sqrt{\frac{a^2+b^2}{2}}$