Question

If positive numbers $a,b,c,d$ are in HP then

• A. $ab\ge cd$
• B. $ac\ge bd$
• C. $ad\ge bc$
• D. $a+d<b+c$

Answer 1

Answer: (C)

$HM$ between $a$ and $c=b$
and $GM=\sqrt{ac}$
Also $HM$ between $b$ and $d=c$
and $GM=\sqrt{bd}$
But $GM>HM$
$\therefore \sqrt{ac}>b$ and $\sqrt{bd}>c$
$\Rightarrow \sqrt{ac}\sqrt{bd}>bc$
$\Rightarrow ad>bc$