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Q.
If positive numbers $a, b, c, d$ are in HP then
Sequences and Series
Solution:
$HM$ between $a$ and $c = b$
and $GM =\sqrt{ ac }$
Also $HM$ between $b$ and $d = c$
and $GM =\sqrt{ bd }$
But $GM > HM$
$\therefore \sqrt{a c}>b$ and $\sqrt{b d}>c$
$\Rightarrow \sqrt{a c} \sqrt{b d}>b c $
$ \Rightarrow a d>b c$