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2013 239 Open Mathematical Olympiad
4
Sqrt inequality with a+b+c<2
Sqrt inequality with a+b+c<2
Source: 239 2013 S4
August 7, 2020
inequalities
algebra
inequalities proposed
Problem Statement
For positive numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfying condition
a
+
b
+
c
<
2
a+b+c<2
a
+
b
+
c
<
2
, Prove that
a
2
+
b
c
+
b
2
+
c
a
+
c
2
+
a
b
<
3.
\sqrt{a^2 +bc}+\sqrt{b^2 +ca}+\sqrt{c^2 + ab}<3.
a
2
+
b
c
+
b
2
+
c
a
+
c
2
+
ab
<
3.
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