# Proving an inequality?

## If a, b, and c are positive numbers and a+b+c=1, prove the inequality a*b+b*c+c*a ≥ 9*a*b*c

$\frac{a + b + c}{3} \ge = \frac{3}{\frac{1}{a} + \frac{1}{b} + \frac{1}{c}}$
$a b + a c + b c \ge 9 a b c$