1952 AMC 12 Question 45
AMC12 · 1952 AMC 12
If $a$ and $b$ are two unequal positive numbers, then:
$\dfrac{2ab}{a+b}\gt\sqrt{ab}\gt\dfrac{a+b}{2}$
$\sqrt{ab}\gt\dfrac{2ab}{a+b}\gt\dfrac{a+b}{2}$
$\dfrac{2ab}{a+b}\gt\dfrac{a+b}{2}\gt\sqrt{ab}$
$\dfrac{a+b}{2}\gt\dfrac{2ab}{a+b}\gt\sqrt{ab}$
$\dfrac{a+b}{2}\gt\sqrt{ab}\gt\dfrac{2ab}{a+b}$