Let $a,b,c$ be positive real numbers, such that: $a+b+c \geq \frac{1}{a}+\frac{1}{b}+\frac{1}{c}.$

Prove that:

\[a+b+c \geq \frac{3}{a+b+c}+\frac{2}{abc}. \]

Let $a,b,c$ be positive real numbers, such that: $a+b+c \geq \frac{1}{a}+\frac{1}{b}+\frac{1}{c}.$

Prove that:

\[a+b+c \geq \frac{3}{a+b+c}+\frac{2}{abc}. \]

Prove that:

\[a+b+c \geq \frac{3}{a+b+c}+\frac{2}{abc}. \]

- Katy729
**Posts:**19**Joined:**Sat May 06, 2017 2:30 am

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