Problem
ALG-B1-M12-P007 Variant 2, Problem 3
#7
★★☆☆☆ Level 2 of 5
If \(a,b>0\), \(a+b=4\), prove \(ab\le4\).
AM-GM.
\(\sqrt{ab}\le\frac{a+b}{2}=2\), hence \(ab\le4\).
Mock olympiad problem. Tags: am-gm.