A) \[{{A}^{2}}=GH\]
B) \[{{H}^{2}}=AG\]
C) \[G=AH\]
D) \[{{G}^{2}}=AH\]
Correct Answer: D
Solution :
Let \[A=\frac{a+b}{2},\ G=\sqrt{ab}\] and \[H=\frac{2ab}{a+b}\]. Then \[{{G}^{2}}=ab\] .....(i) and \[AH=\left( \frac{a+b}{2} \right)\ .\ \frac{2ab}{a+b}=ab\] .....(ii) From (i) and (ii), we have \[{{G}^{2}}=AH\].
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