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Bulgaria Contests
Bulgaria EGMO TST
2017 Bulgaria EGMO TST
3
Linearization bruh
Linearization bruh
Source: Bulgaria EGMO TST 2017 Day 1 Problem 3
February 3, 2023
Tangent Line
Inequality
algebra
Problem Statement
Let
a
a
a
,
b
b
b
,
c
c
c
and
d
d
d
be positive real numbers with
a
+
b
+
c
+
d
=
4
a+b+c+d = 4
a
+
b
+
c
+
d
=
4
. Prove that
a
b
2
+
1
+
b
c
2
+
1
+
c
d
2
+
1
+
d
a
2
+
1
≥
2
\frac{a}{b^2 + 1} + \frac{b}{c^2+1} + \frac{c}{d^2+1} + \frac{d}{a^2+1} \geq 2
b
2
+
1
a
+
c
2
+
1
b
+
d
2
+
1
c
+
a
2
+
1
d
≥
2
.
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