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JBMO TST - Romania
2021 Junior Balkan Team Selection Tests - Romania
P1
Romania Junior TST 2021 Day 3 P1
Romania Junior TST 2021 Day 3 P1
Source:
June 7, 2021
algebra
inequalities
romania
Romanian TST
Problem Statement
Let
a
,
b
,
c
>
0
a,b,c>0
a
,
b
,
c
>
0
be real numbers with the property that
a
+
b
+
c
=
1
a+b+c=1
a
+
b
+
c
=
1
. Prove that
1
a
+
b
c
+
1
b
+
c
a
+
1
c
+
a
b
≥
7
1
+
a
b
c
.
\frac{1}{a+bc}+\frac{1}{b+ca}+\frac{1}{c+ab}\geq\frac{7}{1+abc}.
a
+
b
c
1
+
b
+
c
a
1
+
c
+
ab
1
≥
1
+
ab
c
7
.
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