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MathLinks Contest 6th
1.1
0611 inequality 6th edition Round 1 p1
0611 inequality 6th edition Round 1 p1
Source:
May 3, 2021
inequalities
6th edition
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive real numbers such that
b
c
+
c
a
+
b
=
1
,
bc +ca +b = 1,
b
c
+
c
a
+
b
=
1
,
. Prove that
1
+
b
2
c
2
(
b
+
c
)
2
+
1
+
c
2
a
2
(
c
+
a
)
2
+
1
+
a
2
b
2
(
a
+
b
)
2
≥
5
2
.
\frac {1 +b^2c^2}{(b +c)^2} + \frac {1+ c^2a^2}{(c + a)^2} +\frac {1 +a^2b^2}{(a +b)^2} \geq \frac {5}{2}.
(
b
+
c
)
2
1
+
b
2
c
2
+
(
c
+
a
)
2
1
+
c
2
a
2
+
(
a
+
b
)
2
1
+
a
2
b
2
≥
2
5
.
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