Question

If A, G, H denotes respectively the AM, GM and HM between two unequal positive numbers, then:

• A. $A=G^{2}H$
• B. $G^2=AH$
• C. $A^2=GH$
• D. $A=GH$
• E. none of these

Answer 1

Answer: (B)

Let A, G, H be AM, GM and HM respectively between two unequal numbers a and b. $\therefore$ $A=\frac{a+b}{2}$ ...(i) $G=\sqrt{ab}$ ...(ii) and $H=\frac{2ab}{a+b}$ ?.(iii) $\therefore$ $G^2=AH$