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National and Regional Contests
Moldova Contests
EGMO TST - Moldova
2021 Moldova EGMO TST
1
\frac{a^3+a^2}{1+bc}+\frac{b^3+b^2}{1+ca}+\frac{c^3+c^2}{1+ab}\geq3.
\frac{a^3+a^2}{1+bc}+\frac{b^3+b^2}{1+ca}+\frac{c^3+c^2}{1+ab}\geq3.
Source: Moldova EGMO TST 2021
February 4, 2023
inequalities
Problem Statement
Postive real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfy
a
b
c
=
1
abc=1
ab
c
=
1
. Show that
a
3
+
a
2
1
+
b
c
+
b
3
+
b
2
1
+
c
a
+
c
3
+
c
2
1
+
a
b
≥
3.
\frac{a^3+a^2}{1+bc}+\frac{b^3+b^2}{1+ca}+\frac{c^3+c^2}{1+ab}\geq3.
1
+
b
c
a
3
+
a
2
+
1
+
c
a
b
3
+
b
2
+
1
+
ab
c
3
+
c
2
≥
3.
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