a+b+c>=1/a+1/b+1/c

For discussing Olympiad Level Algebra (and Inequality) problems

a+b+c>=1/a+1/b+1/c

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:
$a+b+c \geq \frac{3}{a+b+c}+\frac{2}{abc}.$
Katy729

Posts: 35
Joined: Sat May 06, 2017 2:30 am

Re: a+b+c>=1/a+1/b+1/c

Someone?
Katy729

Posts: 35
Joined: Sat May 06, 2017 2:30 am

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