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National and Regional Contests
Mexico Contests
Mexico National Olympiad
2007 Mexico National Olympiad
3
Sum of Square Roots Inequality
Sum of Square Roots Inequality
Source: OMM 2007 3
July 19, 2014
inequalities
inequalities unsolved
Problem Statement
Given
a
a
a
,
b
b
b
, and
c
c
c
be positive real numbers with
a
+
b
+
c
=
1
a+b+c=1
a
+
b
+
c
=
1
, prove that
a
+
b
c
+
b
+
c
a
+
c
+
a
b
≤
2
\sqrt{a+bc}+\sqrt{b+ca}+\sqrt{c+ab}\le2
a
+
b
c
+
b
+
c
a
+
c
+
ab
≤
2
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