## Inequality with abc = 1

For discussing Olympiad Level Algebra (and Inequality) problems
Katy729
Posts: 47
Joined: Sat May 06, 2017 2:30 am

### Inequality with abc = 1

Let $x, y, z$ be positive real numbers so that $xyz = 1$. Prove that

$\left( x - 1 + \frac 1y \right) \left( y - 1 + \frac 1z \right) \left( z - 1 + \frac 1x \right) \leq 1.$

asif e elahi
Posts: 183
Joined: Mon Aug 05, 2013 12:36 pm

### Re: Inequality with abc = 1

Hint:

Atonu Roy Chowdhury
Posts: 63
Joined: Fri Aug 05, 2016 7:57 pm