# Thread: Prove the product is less than or equal to 1

1. Let $a,\,b,\,c$ be real numbers greater than $2$ such that $\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=1$.

Prove that $(a-2)(b-2)(c-2)\le 1$.

Well done MarkFL! And thanks for participating in my challenge!

My solution: