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Baltic Way
2008 Baltic Way
2
Inequality with condition
Inequality with condition
Source: Baltic Way 2008
November 12, 2008
inequalities
inequalities unsolved
Problem Statement
Prove that if the real numbers
a
,
b
a,b
a
,
b
and
c
c
c
satisfy
a
2
+
b
2
+
c
2
=
3
a^2+b^2+c^2=3
a
2
+
b
2
+
c
2
=
3
then
a
2
2
+
b
+
c
2
+
b
2
2
+
c
+
a
2
+
c
2
2
+
a
+
b
2
≥
(
a
+
b
+
c
)
2
12
\frac{a^2}{2+b+c^2}+\frac{b^2}{2+c+a^2}+\frac{c^2}{2+a+b^2}\ge\frac{(a+b+c)^2}{12}
2
+
b
+
c
2
a
2
+
2
+
c
+
a
2
b
2
+
2
+
a
+
b
2
c
2
≥
12
(
a
+
b
+
c
)
2
When does the inequality hold?
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