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Poland - Second Round
1957 Poland - Second Round
4
\frac{a}{b + c} + \frac{b}{c+ a} + \frac{c}{a+b} \geq \frac{3}{2}
\frac{a}{b + c} + \frac{b}{c+ a} + \frac{c}{a+b} \geq \frac{3}{2}
Source: Polish MO second round 1957 p4
August 29, 2024
algebra
inequalities
Problem Statement
Prove that if
a
>
0
a > 0
a
>
0
,
b
>
0
b > 0
b
>
0
,
c
>
0
c > 0
c
>
0
, then
a
b
+
c
+
b
c
+
a
+
c
a
+
b
≥
3
2
.
\frac{a}{b + c} + \frac{b}{c+ a} + \frac{c}{a+b} \geq \frac{3}{2}.
b
+
c
a
+
c
+
a
b
+
a
+
b
c
≥
2
3
.
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