# Mathematics Equality Proof

Positive numbers a, b, c satisfy $1/a + 1/b + 1/c = 3$.

a) Prove that $abc \ge 1$.

b) Prove that $(a+b)(a+c)(b+c) \ge 8$. When does the equality hold?

I want to say that I will be using conjugates for part a to prove the inequality is true. I am not sure about part b...

a) Use $GM \ge HM$
b) Use $a+b \ge 2\sqrt{ab}$ for each factor.