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Binomial Expression

HM of two pos...

Question

HM of two positive real numbers a & b is

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Solution

The correct options are
B
D

AM $\geq$ GM $\geq$ HM

So, $\frac{a + b}{2}$ $\geq$ $\sqrt{a b}$ $\geq$ $\frac{2 a b}{a + b}$

$\Rightarrow$ $\frac{2 a b}{a + b}$ $\leq$ $\sqrt{a b}$

Also, $\frac{2 a b}{a + b}$ $\leq$ $\frac{a + b}{2}$

So, B & D are true

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