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Poland Contests
Poland - Second Round
1961 Poland - Second Round
5
5
Part of
1961 Poland - Second Round
Problems
(1)
a + b + c> 0, ab + b, c + ca > 0, abc > 0
Source: : Polish MO Second Round 1961 p5
8/31/2024
Prove that if the real numbers
a
a
a
,
b
b
b
,
c
c
c
satisfy the inequalities
a
+
b
+
c
>
0
,
a + b + c> 0,
a
+
b
+
c
>
0
,
a
b
+
b
c
+
c
a
>
0
ab + bc + ca > 0
ab
+
b
c
+
c
a
>
0
a
b
c
>
0
abc > 0
ab
c
>
0
then
a
>
0
,
b
>
0
,
c
>
0
a > 0, b > 0, c > 0
a
>
0
,
b
>
0
,
c
>
0
.
algebra
System
inequalities