a+b+c>=1/a+1/b+1/c
Posted: 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:
\[a+b+c \geq \frac{3}{a+b+c}+\frac{2}{abc}. \]
Prove that:
\[a+b+c \geq \frac{3}{a+b+c}+\frac{2}{abc}. \]