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Jozsef Wildt International Math Competition
2019 Jozsef Wildt International Math Competition
W. 24
Proove this inequality
Proove this inequality
Source: 2019 Jozsef Wildt International Math Competition-W. 24
May 18, 2020
inequalities
Problem Statement
If
a
a
a
,
b
b
b
,
c
>
0
c > 0
c
>
0
, prove that
a
b
+
c
+
b
c
+
a
+
c
a
+
b
≥
a
+
b
a
+
b
+
2
c
+
b
+
c
2
a
+
b
+
c
+
c
+
a
a
+
2
b
+
c
\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\geq \frac{a+b}{a+b+2c}+\frac{b+c}{2a+b+c}+\frac{c+a}{a+2b+c}
b
+
c
a
+
c
+
a
b
+
a
+
b
c
≥
a
+
b
+
2
c
a
+
b
+
2
a
+
b
+
c
b
+
c
+
a
+
2
b
+
c
c
+
a
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