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Contests
National and Regional Contests
Russia Contests
Russian Team Selection Tests
Russian TST 2018
P1
Inequality
Inequality
Source: Russian TST 2018, Day 10 P1 (Groups A & B)
March 30, 2023
algebra
inequalities
Problem Statement
Let
a
,
b
,
c
a,b,c{}
a
,
b
,
c
be positive real numbers. Prove that
108
⋅
(
a
b
+
b
c
+
c
a
)
⩽
(
a
+
b
+
b
+
c
+
c
+
a
)
4
.
108\cdot(ab+bc+ca)\leqslant(\sqrt{a+b}+\sqrt{b+c}+\sqrt{c+a})^4.
108
⋅
(
ab
+
b
c
+
c
a
)
⩽
(
a
+
b
+
b
+
c
+
c
+
a
)
4
.
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