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2011 JBMO Shortlist
3
Simple inequality
Simple inequality
Source: JBMO 2011 Shortlist A3
May 15, 2016
inequalities
algebra
JBMO Shortlist
High school olympiad
Problem Statement
A3
\boxed{\text{A3}}
A3
If
a
,
b
a,b
a
,
b
be positive real numbers, show that:
a
2
+
a
b
+
b
2
3
+
a
b
≤
a
+
b
\displaystyle{\sqrt{\dfrac{a^2+ab+b^2}{3}}+\sqrt{ab}\leq a+b}
3
a
2
+
ab
+
b
2
+
ab
≤
a
+
b
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