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National and Regional Contests
Switzerland Contests
Switzerland Team Selection Test
2020 Switzerland Team Selection Test
12
Tournament S.S.D
Tournament S.S.D
Source:
June 2, 2021
InInquility
algebra
Problem Statement
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be positive real numbers such that
a
+
b
+
c
+
d
=
1
a+b+c+d=1
a
+
b
+
c
+
d
=
1
prove that: (
a
2
a
+
b
+
b
2
b
+
c
+
c
2
c
+
d
+
d
2
d
+
a
)
5
≥
5
5
(
a
c
27
)
2
\frac{a^2}{a+b}+\frac{b^2}{b+c}+\frac{c^2}{c+d}+\frac{d^2}{d+a})^5 \geq 5^5(\frac{ac}{27})^2
a
+
b
a
2
+
b
+
c
b
2
+
c
+
d
c
2
+
d
+
a
d
2
)
5
≥
5
5
(
27
a
c
)
2
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