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Tournament Of Towns
1985 Tournament Of Towns
(092) T3
TOT 092 1985 Spring Train S3 a+b+c>0 , bc+ca+ab>0, abc>0 => a,b,c>0
TOT 092 1985 Spring Train S3 a+b+c>0 , bc+ca+ab>0, abc>0 => a,b,c>0
Source:
August 24, 2019
algebra
inequalities
Problem Statement
Three real numbers
a
,
b
a, b
a
,
b
and
c
c
c
are given . It is known that
a
+
b
+
c
>
0
,
b
c
+
c
a
+
a
b
>
0
a + b + c >0 , bc+ ca + ab > 0
a
+
b
+
c
>
0
,
b
c
+
c
a
+
ab
>
0
and
a
b
c
>
0
abc > 0
ab
c
>
0
. Prove that
a
>
0
,
b
>
0
a > 0 , b > 0
a
>
0
,
b
>
0
and
c
>
0
c > 0
c
>
0
.
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