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National and Regional Contests
Germany Contests
Germany Team Selection Test
2010 Germany Team Selection Test
2
(4a+b)/(a+4b) + (4b+c)/(b+4c) + (4c+a)/(c+4a)
(4a+b)/(a+4b) + (4b+c)/(b+4c) + (4c+a)/(c+4a)
Source: VAIMO 2, German Pre-TST 2010
July 16, 2011
inequalities
inequalities unsolved
Problem Statement
Prove or disprove that
∀
a
,
b
,
c
,
d
∈
R
+
\forall a,b,c,d \in \mathbb{R}^+
∀
a
,
b
,
c
,
d
∈
R
+
we have the following inequality:
3
≤
4
a
+
b
a
+
4
b
+
4
b
+
c
b
+
4
c
+
4
c
+
a
c
+
4
a
<
33
4
3 \leq \frac{4a+b}{a+4b} + \frac{4b+c}{b+4c} + \frac{4c+a}{c+4a} < \frac{33}{4}
3
≤
a
+
4
b
4
a
+
b
+
b
+
4
c
4
b
+
c
+
c
+
4
a
4
c
+
a
<
4
33
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