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Inequality with a^2+b^2+c^2=1; P4 : B&H TST 2002
Inequality with a^2+b^2+c^2=1; P4 : B&H TST 2002
Source:
October 31, 2014
inequalities
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be real numbers such that
a
2
+
b
2
+
c
2
=
1
a^2+b^2+c^2=1
a
2
+
b
2
+
c
2
=
1
. Prove that
a
2
1
+
2
b
c
+
b
2
1
+
2
c
a
+
c
2
1
+
2
a
b
≥
3
5
\frac{a^2}{1+2bc}+\frac{b^2}{1+2ca}+\frac{c^2}{1+2ab} \ge \frac35
1
+
2
b
c
a
2
+
1
+
2
c
a
b
2
+
1
+
2
ab
c
2
≥
5
3
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