Problem
ALG-B2-M02-P001 One variable
#1
★★☆☆☆ Level 2 of 5
For \(x>0\), prove \(x+\frac{36}{x}\ge12\).
Hint 1. Take two positive terms.
Hint 2. Their product is \(36\).
By AM-GM, \(x+\frac{36}{x}\ge2\sqrt{x\cdot\frac{36}{x}}=12\). Equality occurs at \(x=6\).
AM-GM module training problem. Method tags: am-gm, equality-case.