SEAMO 2027 - Paper F - SET 07 - Self-study Question 17

Let $A,G,H$ be respectively the arithmetic, geometric and harmonic means of two unequal positive numbers. Which statement(s) are true?

(i) $AG=H^2$; (ii) $AH=G^2$; (iii) $A>H>G$; (iv) $A>G>H$.