Problem
ALG-B1-M11-P008 Reciprocal
#8
★★☆☆☆ Level 2 of 5
For \(x>0\), prove \(x+\frac{9}{x}\ge6\).
Equality is expected at \(x=3\).
By AM-GM, \(x+\frac{9}{x}\ge2\sqrt{9}=6\).
Strategy: the equality case points to AM-GM.