Problem
ALG-B1-M12-P019 Variant 5, Problem 3
#19
★★★★☆ Level 4 of 5
If \(x,y,z>0\), \(xyz=1\), prove \((1+x)(1+y)(1+z)\ge8\).
\(1+x\ge2\sqrt{x}\).
Multiplying the three estimates gives \(8\sqrt{xyz}=8\).
Mock olympiad problem. Tags: am-gm.