For discussing Olympiad Level Algebra (and Inequality) problems
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Post Number:#1  Unread postby Katy729 » Sat Jul 01, 2017 3:31 pm

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