Question 94
For positive numbers $x$, $y$, $z$, satisfying equality $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 3$, prove that the following inequality is true:
$$(x-1)(y-1)(z-1) \le \frac{1}{4}(xyz-1).$$
(Vadim Mitrofanov)
$$(x-1)(y-1)(z-1) \le \frac{1}{4}(xyz-1).$$
(Vadim Mitrofanov)