Show that \left ( a+b+c \right )\left ( \frac{1}{a}+ \frac{1}{b}+\frac{1}{c} \right )\geq 9

Solution:

⇨We have to show that

$Show that \left ( a+b+c \right )\left ( \frac{1}{a}+ \frac{1}{b}+\frac{1}{c} \right )\geq 9$

⇨If a, b, c>0 then Arithmetic Mean $Show that \left ( a+b+c \right )\left ( \frac{1}{a}+ \frac{1}{b}+\frac{1}{c} \right )\geq 9$
⇨If a, b, c>0 then Geometric Mean $Show that \left ( a+b+c \right )\left ( \frac{1}{a}+ \frac{1}{b}+\frac{1}{c} \right )\geq 9$
⇨Now $Show that \left ( a+b+c \right )\left ( \frac{1}{a}+ \frac{1}{b}+\frac{1}{c} \right )\geq 9$

$Show that \left ( a+b+c \right )\left ( \frac{1}{a}+ \frac{1}{b}+\frac{1}{c} \right )\geq 9$
$Show that \left ( a+b+c \right )\left ( \frac{1}{a}+ \frac{1}{b}+\frac{1}{c} \right )\geq 9$

⇨Now (i) x (ii)

$Show that \left ( a+b+c \right )\left ( \frac{1}{a}+ \frac{1}{b}+\frac{1}{c} \right )\geq 9$
$Show that \left ( a+b+c \right )\left ( \frac{1}{a}+ \frac{1}{b}+\frac{1}{c} \right )\geq 9$
$Show that \left ( a+b+c \right )\left ( \frac{1}{a}+ \frac{1}{b}+\frac{1}{c} \right )\geq 9$
$Show that \left ( a+b+c \right )\left ( \frac{1}{a}+ \frac{1}{b}+\frac{1}{c} \right )\geq 9$ Proved

Show that \left ( a+b+c \right )\left ( \frac{1}{a}+ \frac{1}{b}+\frac{1}{c} \right )\geq 9

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