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Inequality involving square roots
Inequality involving square roots
Source: Bulgarian IMO TST 2004, Day 4, Problem 2
July 8, 2013
inequalities
algebra
Inequality
Problem Statement
Prove that if
a
,
b
,
c
≥
1
a,b,c \ge 1
a
,
b
,
c
≥
1
and
a
+
b
+
c
=
9
a+b+c=9
a
+
b
+
c
=
9
, then
a
b
+
b
c
+
c
a
≤
a
+
b
+
c
\sqrt{ab+bc+ca} \le \sqrt{a} +\sqrt{b} + \sqrt{c}
ab
+
b
c
+
c
a
≤
a
+
b
+
c
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